Kirillov, A. A. (Aleksandr Aleksandrovich) 1936
Overview
Works:  51 works in 294 publications in 8 languages and 4,307 library holdings 

Genres:  Conference papers and proceedings 
Roles:  Author, Editor, Honoree, ed, Dedicatee, Translator, Other 
Classifications:  QA556, 512.55 
Publication Timeline
.
Most widely held works by
A. A Kirillov
The method of coordinates by
I. M Gelʹfand(
Book
)
35 editions published between 1964 and 2002 in 3 languages and held by 784 WorldCat member libraries worldwide
35 editions published between 1964 and 2002 in 3 languages and held by 784 WorldCat member libraries worldwide
Elements of the theory of representations by
A. A Kirillov(
Book
)
42 editions published between 1972 and 2012 in 5 languages and held by 614 WorldCat member libraries worldwide
The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the Englishreading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The trans lation is in all essential respects faithful to the original Russian. The translator records his gratitude to Linda Sax, who typed the entire translation, to Laura Larsson, who prepared the bibliography (considerably modified from the original), and to Betty Underhill, who rendered essential assistance
42 editions published between 1972 and 2012 in 5 languages and held by 614 WorldCat member libraries worldwide
The translator of a mathematical work faces a task that is at once fascinating and frustrating. He has the opportunity of reading closely the work of a master mathematician. He has the duty of retaining as far as possible the flavor and spirit of the original, at the same time rendering it into a readable and idiomatic form of the language into which the translation is made. All of this is challenging. At the same time, the translator should never forget that he is not a creator, but only a mirror. His own viewpoints, his own preferences, should never lead him into altering the original, even with the best intentions. Only an occasional translator's note is permitted. The undersigned is grateful for the opportunity of translating Professor Kirillov's fine book on group representations, and hopes that it will bring to the Englishreading mathematical public as much instruction and interest as it has brought to the translator. Deviations from the Russian text have been rigorously avoided, except for a number of corrections kindly supplied by Professor Kirillov. Misprints and an occasional solecism have been tacitly taken care of. The trans lation is in all essential respects faithful to the original Russian. The translator records his gratitude to Linda Sax, who typed the entire translation, to Laura Larsson, who prepared the bibliography (considerably modified from the original), and to Betty Underhill, who rendered essential assistance
Theorems and problems in functional analysis by
A. A Kirillov(
Book
)
37 editions published between 1979 and 2013 in 5 languages and held by 591 WorldCat member libraries worldwide
Even the simplest mathematical abstraction of the phenomena of reality the real linecan be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures
37 editions published between 1979 and 2013 in 5 languages and held by 591 WorldCat member libraries worldwide
Even the simplest mathematical abstraction of the phenomena of reality the real linecan be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply" operations," and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its" continuity" as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures
Representation theory and noncommutative harmonic analysis I : fundamental concepts, representations of Virasoro and affine
algebras by
A. A Kirillov(
Book
)
22 editions published between 1994 and 2011 in English and held by 301 WorldCat member libraries worldwide
Part I of this book is a short review of the classical part of representation theory. The main chapters of representation theory are discussed: representations of finite and compact groups, finite and infinitedimensional representations of Lie groups. It is a typical feature of this survey that the structure of the theory is carefully exposed  the reader can easily see the essence of the theory without being overwhelmed by details. The final chapter is devoted to the method of orbits for different types of groups. Part II deals with representation of Virasoro and KacMoody algebra. The second part of the book deals with representations of Virasoro and KacMoody algebra. The wealth of recent results on representations of infinitedimensional groups is presented
22 editions published between 1994 and 2011 in English and held by 301 WorldCat member libraries worldwide
Part I of this book is a short review of the classical part of representation theory. The main chapters of representation theory are discussed: representations of finite and compact groups, finite and infinitedimensional representations of Lie groups. It is a typical feature of this survey that the structure of the theory is carefully exposed  the reader can easily see the essence of the theory without being overwhelmed by details. The final chapter is devoted to the method of orbits for different types of groups. Part II deals with representation of Virasoro and KacMoody algebra. The second part of the book deals with representations of Virasoro and KacMoody algebra. The wealth of recent results on representations of infinitedimensional groups is presented
Lectures on the orbit method by
A. A Kirillov(
Book
)
12 editions published between 1900 and 2004 in English and held by 272 WorldCat member libraries worldwide
Isaac Newton encrypted his discoveries in analysis in the form of an anagram, which deciphers to the sentence ``It is worthwhile to solve differential equations''. Accordingly, one can express the main idea behind the Orbit Method by saying "It is worthwhile to study coadjoint orbits". The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for nonexperts and gives the first systematic, detailed, and selfcontained exposition of the method. It starts with a convenient ``User's Guide'' and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for nonexperts and a reference book for research mathematicians and mathematical physicists
12 editions published between 1900 and 2004 in English and held by 272 WorldCat member libraries worldwide
Isaac Newton encrypted his discoveries in analysis in the form of an anagram, which deciphers to the sentence ``It is worthwhile to solve differential equations''. Accordingly, one can express the main idea behind the Orbit Method by saying "It is worthwhile to study coadjoint orbits". The orbit method was introduced by the author, A. A. Kirillov, in the 1960s and remains a useful and powerful tool in areas such as Lie theory, group representations, integrable systems, complex and symplectic geometry, and mathematical physics. This book describes the essence of the orbit method for nonexperts and gives the first systematic, detailed, and selfcontained exposition of the method. It starts with a convenient ``User's Guide'' and contains numerous examples. It can be used as a text for a graduate course, as well as a handbook for nonexperts and a reference book for research mathematicians and mathematical physicists
Representation theory and noncommutative harmonic analysis II by
A. A Kirillov(
Book
)
16 editions published in 1995 in English and held by 244 WorldCat member libraries worldwide
This EMS volume contains two contributions: the first one, "Harmonic Analysis on Homogeneous Spaces", is written by V.F. Molchanov, the second one, "Representations of Lie Groups and Special Functions", by N. Ya. Vilenkin and A.U. Klimyk. Molchanov focuses on harmonic analysis on semisimple spaces, whereas Vilenkin and Klimyk treat group theoretical methods also with respect to integral transforms. Both contributions are surveys introducing readers to the above topics and preparing them for the study of more specialised literature. This book will be very useful to mathematicians, theoretical physicists and also to chemists dealing with quantum systems
16 editions published in 1995 in English and held by 244 WorldCat member libraries worldwide
This EMS volume contains two contributions: the first one, "Harmonic Analysis on Homogeneous Spaces", is written by V.F. Molchanov, the second one, "Representations of Lie Groups and Special Functions", by N. Ya. Vilenkin and A.U. Klimyk. Molchanov focuses on harmonic analysis on semisimple spaces, whereas Vilenkin and Klimyk treat group theoretical methods also with respect to integral transforms. Both contributions are surveys introducing readers to the above topics and preparing them for the study of more specialised literature. This book will be very useful to mathematicians, theoretical physicists and also to chemists dealing with quantum systems
The orbit method in geometry and physics : in honor of A.A. Kirillov by
Christian Duval(
Book
)
13 editions published in 2003 in English and Undetermined and held by 220 WorldCat member libraries worldwide
The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses
13 editions published in 2003 in English and Undetermined and held by 220 WorldCat member libraries worldwide
The orbit method influenced the development of several areas of mathematics in the second half of the 20th century and remains a useful and powerful tool in such areas as Lie theory, representation theory, integrable systems, complex geometry, and mathematical physics. Among the distinguished names associated with the orbit method is that of A.A. Kirillov, whose pioneering paper on nilpotent orbits (1962), places him as the founder of orbit theory. The original research papers in this volume are written by prominent mathematicians and reflect recent achievements in orbit theory and other closely related areas such as harmonic analysis, classical representation theory, Lie superalgebras, Poisson geometry, and quantization. Contributors: A. Alekseev, J. Alev, V. Baranovksy, R. Brylinski, J. Dixmier, S. Evens, D.R. Farkas, V. Ginzburg, V. Gorbounov, P. Grozman, E. Gutkin, A. Joseph, D. Kazhdan, A.A. Kirillov, B. Kostant, D. Leites, F. Malikov, A. Melnikov, P.W. Michor, Y.A. Neretin, A. Okounkov, G. Olshanski, F. Petrov, A. Polishchuk, W. Rossmann, A. Sergeev, V. Schechtman, I. Shchepochkina. The work will be an invaluable reference for researchers in the above mentioned fields, as well as a useful text for graduate seminars and courses
Kirillov's seminar on representation theory by Representation theory (Kirillov's seminar)(
Book
)
4 editions published in 1998 in English and held by 179 WorldCat member libraries worldwide
4 editions published in 1998 in English and held by 179 WorldCat member libraries worldwide
Representations of Lie groups and Lie algebras by
A. A Kirillov(
Book
)
10 editions published in 1985 in English and held by 146 WorldCat member libraries worldwide
10 editions published in 1985 in English and held by 146 WorldCat member libraries worldwide
Topics in representation theory(
Book
)
7 editions published in 1991 in English and held by 145 WorldCat member libraries worldwide
7 editions published in 1991 in English and held by 145 WorldCat member libraries worldwide
A tale of two fractals by
A. A Kirillov(
Book
)
12 editions published in 2013 in English and held by 73 WorldCat member libraries worldwide
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals helps bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, nonspecialist mathematicians a solid foundation in the theory of fractals. As its title suggests, this book focuses primarily on two fractals: the Sierpiński gasket and the Apollonian gasket. Over the course of the book, they are developed and discussed in various contexts. Along with fundamental definitions and properties, some of the key concepts and approaches covered include * the Laplace operator * harmonic functions * generalized numerical systems * Descartes' theorem * rational paramaterizations * group action on fractals * generalization to multiple dimensions In addition to its explicit goal of providing undergraduate and graduate students with a sound foundation in fractal theory, A Tale of Two Fractals serves to enhance their overall understanding of mathematics by drawing on a wide variety of techniques from other subfields. Furthermore, by virtue of the subject matter, it provides a unique opportunity for students to develop their capacity for recognizing patterns and formulating interesting questions. It is therefore a valuable text not only for any course on fractals or hyperbolic geometry, but also for any survey course with an aim of honing creativeproblemsolving skills
12 editions published in 2013 in English and held by 73 WorldCat member libraries worldwide
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals helps bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, nonspecialist mathematicians a solid foundation in the theory of fractals. As its title suggests, this book focuses primarily on two fractals: the Sierpiński gasket and the Apollonian gasket. Over the course of the book, they are developed and discussed in various contexts. Along with fundamental definitions and properties, some of the key concepts and approaches covered include * the Laplace operator * harmonic functions * generalized numerical systems * Descartes' theorem * rational paramaterizations * group action on fractals * generalization to multiple dimensions In addition to its explicit goal of providing undergraduate and graduate students with a sound foundation in fractal theory, A Tale of Two Fractals serves to enhance their overall understanding of mathematics by drawing on a wide variety of techniques from other subfields. Furthermore, by virtue of the subject matter, it provides a unique opportunity for students to develop their capacity for recognizing patterns and formulating interesting questions. It is therefore a valuable text not only for any course on fractals or hyperbolic geometry, but also for any survey course with an aim of honing creativeproblemsolving skills
Homogeneous spaces, representations and special functions(
Book
)
3 editions published in 1995 in English and Undetermined and held by 22 WorldCat member libraries worldwide
3 editions published in 1995 in English and Undetermined and held by 22 WorldCat member libraries worldwide
Introduction to superanalysis by
F. A Berezin(
Book
)
8 editions published in 1987 in English and Dutch and held by 20 WorldCat member libraries worldwide
TO SUPERANAL YSIS Edited by A.A. KIRILLOV Translated from the Russian by J. Niederle and R. Kotecky English translation edited and revised by Dimitri Leites SPRINGERSCIENCE+BUSINESS MEDIA, B.V. Library of Congress CataloginginPublication Data Berezin, F.A. (Feliks Aleksandrovich) Introduction to superanalysis. (Mathematical physics and applied mathematics; v. 9) Part I is translation of: Vvedenie v algebru i analiz s antikommutirurushchimi peremennymi. Bibliography: p. Includes index. 1. Mathetical analysis. I. Title. II. Title: Superanalysis. III. Series. QA300. B459 1987 530. 15'5 8716293 ISBN 9789048183920 ISBN 9789401719636 (eBook) DOI 10. 1007/9789401719636 All Rights Reserved © 1987 by Springer Science+Business Media Dordrecht Originally published by D. Reidel Publishing Company, Dordrecht, Holland in 1987 No part of the material protected by this copyright notice may be reproduced in whole or in part or utilized in any form or by any means electronic or mechanical including photocopying recording or storing in any electronic information system without first obtaining the written permission of the copyright owner. CONTENTS EDITOR'S FOREWORD ix INTRODUCTION 1 1. The Sources 1 2. Supermanifolds 3 3. Additional Structures on Supermanifolds 11 4. Representations of Lie Superalgebras and Supergroups 21 5. Conclusion 23 References 24 PART I CHAPTER 1. GRASSMANN ALGEBRA 29 1. Basic Facts on Associative Algebras 29 2. Grassmann Algebras 35 3. Algebras A(U) 55 CHAPTER 2. SUPERANAL YSIS 74 1. Derivatives 74 2. Integral 76 CHAPTER 3. LINEAR ALGEBRA IN ZzGRADED SPACES 90 1
8 editions published in 1987 in English and Dutch and held by 20 WorldCat member libraries worldwide
TO SUPERANAL YSIS Edited by A.A. KIRILLOV Translated from the Russian by J. Niederle and R. Kotecky English translation edited and revised by Dimitri Leites SPRINGERSCIENCE+BUSINESS MEDIA, B.V. Library of Congress CataloginginPublication Data Berezin, F.A. (Feliks Aleksandrovich) Introduction to superanalysis. (Mathematical physics and applied mathematics; v. 9) Part I is translation of: Vvedenie v algebru i analiz s antikommutirurushchimi peremennymi. Bibliography: p. Includes index. 1. Mathetical analysis. I. Title. II. Title: Superanalysis. III. Series. QA300. B459 1987 530. 15'5 8716293 ISBN 9789048183920 ISBN 9789401719636 (eBook) DOI 10. 1007/9789401719636 All Rights Reserved © 1987 by Springer Science+Business Media Dordrecht Originally published by D. Reidel Publishing Company, Dordrecht, Holland in 1987 No part of the material protected by this copyright notice may be reproduced in whole or in part or utilized in any form or by any means electronic or mechanical including photocopying recording or storing in any electronic information system without first obtaining the written permission of the copyright owner. CONTENTS EDITOR'S FOREWORD ix INTRODUCTION 1 1. The Sources 1 2. Supermanifolds 3 3. Additional Structures on Supermanifolds 11 4. Representations of Lie Superalgebras and Supergroups 21 5. Conclusion 23 References 24 PART I CHAPTER 1. GRASSMANN ALGEBRA 29 1. Basic Facts on Associative Algebras 29 2. Grassmann Algebras 35 3. Algebras A(U) 55 CHAPTER 2. SUPERANAL YSIS 74 1. Derivatives 74 2. Integral 76 CHAPTER 3. LINEAR ALGEBRA IN ZzGRADED SPACES 90 1
Oblastnoĭ dramaticheskiĭ : povestʹ by
Aleksandr Kirillov(
Book
)
3 editions published in 1987 in Russian and held by 15 WorldCat member libraries worldwide
3 editions published in 1987 in Russian and held by 15 WorldCat member libraries worldwide
Representation theory and noncommutative harmonic analysis(
Book
)
4 editions published between 1994 and 1995 in English and German and held by 13 WorldCat member libraries worldwide
4 editions published between 1994 and 1995 in English and German and held by 13 WorldCat member libraries worldwide
Sur les corps liés aux algèbres enveloppantes des algèbres de lie by
I. M Gelʹfand(
Book
)
6 editions published between 1966 and 1967 in French and English and held by 10 WorldCat member libraries worldwide
6 editions published between 1966 and 1967 in French and English and held by 10 WorldCat member libraries worldwide
Summer School on Group Representations by
Summer School on Group Representations(
Book
)
1 edition published in 1985 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1985 in English and held by 8 WorldCat member libraries worldwide
El método de coordenadas by
I. M Gelʹfand(
Book
)
4 editions published between 1968 and 1981 in 3 languages and held by 7 WorldCat member libraries worldwide
4 editions published between 1968 and 1981 in 3 languages and held by 7 WorldCat member libraries worldwide
Differencialʹnye formy v algebraičeskoj topologii by
Raoul Bott(
Book
)
2 editions published in 1989 in Russian and held by 6 WorldCat member libraries worldwide
2 editions published in 1989 in Russian and held by 6 WorldCat member libraries worldwide
Predely by
A. A Kirillov(
Book
)
4 editions published between 1968 and 1973 in Russian and held by 6 WorldCat member libraries worldwide
4 editions published between 1968 and 1973 in Russian and held by 6 WorldCat member libraries worldwide
more
fewer
Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Gelʹfand, I. M. (Izrailʹ Moiseevich) Author
 Glagoleva, E. G. (Elena Georgievna)
 Gvishiani, A. D.
 Duval, Christian Editor
 Ovsienko, Valentin Editor
 Guieu, Laurent Editor
 Sosinskiĭ, A. B. (Alekseĭ Bronislavovich) Translator
 Silverman, Richard A. Author
 Olshanskiǐ, G. I. (Grigori I.) Editor
 Bolyai János Matematikai Társulat
Useful Links
Associated Subjects
Affine algebraic groups Algebra Algebraic topology Calculus Cell aggregationMathematics Chemistry Coordinates Differential forms Differential topology Fractals Functional analysis Functions, Special Geometry Geometry, Algebraic Global analysis (Mathematics) Global differential geometry Group theory Harmonic analysis Hyperspace KacMoody algebras Lie algebras Lie groups Mathematical analysis Mathematical physics Mathematics Orbit method Physics Quantum theory Representations of algebras Representations of groups Representations of Lie algebras Representations of Lie groups Rings (Algebra) Topological groups Visualization
Alternative Names
Aleksandr Kirillov matematico russo
Aleksandr Kirillov russisk matematikar
Aleksandr Kirillov russisk matematiker
Aleksandr Kirílov
Alexander Alexandrowitsch Kirillow russischer Mathematiker
Alexandre Kirillov mathématicien russe
Alexandre Kirillov Russian mathematician
Alexandre Kirillov Russisch wiskundige
Kirillov, A.
Kirillov, A. A.
Kirillov, A.A. 1936
Kirillov, Aleksandar A.
Kirillov, Aleksandr Aleksandrovič
Kirillov, Aleksandr Aleksandrovič 1936
Kirillov, Aleksandr Aleksandrovich.
Kirillov Aleksandr Aleksandrovich 1936....
Kirillov Aleksandr Aleksandrovitch 1936....
Kirillov, Alexander 1936
Kirillov, Alexander A. 1936
Kirillov, Alexandr A. 1936
Kirillov, Alexandre 1936
Kirillov, Alexandre Alexandrovitch 1936
Kirillow, A. A. 1936
Kirillow, Aleksandr Aleksandrovič 1936
Kirillow, Alexander Alexandrowitsch 1936
Кириллов, А. А..
Кириллов, Александр Александрович.
アレクサンドル・キリロフ
キリーロフ, A. A
亞歷山大·卡里洛夫
Languages
Covers