Neeb, KarlHermann
Overview
Works:  156 works in 334 publications in 3 languages and 3,404 library holdings 

Roles:  Author, Editor, Creator, Other 
Classifications:  QA3, 512.55 
Publication Timeline
.
Most widely held works by
KarlHermann Neeb
Lie semigroups and their applications by
Joachim Hilgert(
Book
)
17 editions published in 1993 in English and held by 346 WorldCat member libraries worldwide
Subsemigroups of finitedimensional Lie groups that are generated by oneparameter semigroups are the subject of this book. It covers basic Lie theory for such semigroups and some closely related topics. These include ordered homogeneous manifolds, where the order is defined by a field of cones, invariant cones in Lie algebras and associated Ol'shanskii semigroups. Applications to representation theory, symplectic geometry and Hardy spaces are also given. The book is written as an efficient guide for those interested in subsemigroups of Lie groups and their applications in various fields of mathematics (see the User's guide at the end of the Introduction). Since it is essentially selfcontained and leads directly to the core of the theory, the first part of the book can also serve as an introduction to the subject. The reader is merely expected to be familiar with the basic theory of Lie groups and Lie algebras
17 editions published in 1993 in English and held by 346 WorldCat member libraries worldwide
Subsemigroups of finitedimensional Lie groups that are generated by oneparameter semigroups are the subject of this book. It covers basic Lie theory for such semigroups and some closely related topics. These include ordered homogeneous manifolds, where the order is defined by a field of cones, invariant cones in Lie algebras and associated Ol'shanskii semigroups. Applications to representation theory, symplectic geometry and Hardy spaces are also given. The book is written as an efficient guide for those interested in subsemigroups of Lie groups and their applications in various fields of mathematics (see the User's guide at the end of the Introduction). Since it is essentially selfcontained and leads directly to the core of the theory, the first part of the book can also serve as an introduction to the subject. The reader is merely expected to be familiar with the basic theory of Lie groups and Lie algebras
Invariant subsemigroups of Lie groups by
KarlHermann Neeb(
Book
)
17 editions published between 1990 and 1993 in 3 languages and held by 241 WorldCat member libraries worldwide
17 editions published between 1990 and 1993 in 3 languages and held by 241 WorldCat member libraries worldwide
Holomorphy and convexity in Lie theory by
KarlHermann Neeb(
Book
)
2 editions published in 2000 in English and held by 133 WorldCat member libraries worldwide
2 editions published in 2000 in English and held by 133 WorldCat member libraries worldwide
Developments and trends in infinitedimensional lie theory by
KarlHermann Neeb(
Book
)
15 editions published between 2010 and 2011 in English and held by 128 WorldCat member libraries worldwide
This collection of invited expository articles focuses on recent developments and trends in infinitedimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinitedimensional Lie (super )algebras, geometry of infinitedimensional Lie (transformation) groups, and representation theory of infinitedimensional Lie groups. Part (A) is mainly concerned with the structure and representation theory of infinitedimensional Lie algebras and contains articles on the structure of directlimit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac{u2013}Moody superalgebras. The articles in Part (B) examine connections between infinitedimensional Lie theory and geometry. The topics range from infinitedimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordantheoretic geometries and new results on directlimit groups. The analytic representation theory of infinitedimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach{u2013}Lie{u2013}Poisson spaces, and infinitedimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf
15 editions published between 2010 and 2011 in English and held by 128 WorldCat member libraries worldwide
This collection of invited expository articles focuses on recent developments and trends in infinitedimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinitedimensional Lie (super )algebras, geometry of infinitedimensional Lie (transformation) groups, and representation theory of infinitedimensional Lie groups. Part (A) is mainly concerned with the structure and representation theory of infinitedimensional Lie algebras and contains articles on the structure of directlimit Lie algebras, extended affine Lie algebras and loop algebras, as well as representations of loop algebras and Kac{u2013}Moody superalgebras. The articles in Part (B) examine connections between infinitedimensional Lie theory and geometry. The topics range from infinitedimensional groups acting on fiber bundles, corresponding characteristic classes and gerbes, to Jordantheoretic geometries and new results on directlimit groups. The analytic representation theory of infinitedimensional Lie groups is still very much underdeveloped. The articles in Part (C) develop new, promising methods based on heat kernels, multiplicity freeness, Banach{u2013}Lie{u2013}Poisson spaces, and infinitedimensional generalizations of reductive Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf
Structure and geometry of Lie groups by
Joachim Hilgert(
Book
)
21 editions published between 2011 and 2015 in English and held by 121 WorldCat member libraries worldwide
This text is designed as an introduction to Lie groups and their actions on manifolds, one that is accessible both to a broad range of mathematicians and to graduate students.℗¡Building on℗¡the authors' LieGruppen und LieAlgebren textbook from 1991, it℗¡presents the fundamental℗¡ principles of Lie groups℗¡while incorporating the past 20 years of the authors' teaching and research, and giving due emphasis to the role played by differential geometry in the field. The text is entirely self contained,℗¡and provides ample guidance to students with the presence of many exercises and selected hints. The work begins with a study of matrix groups, which serve as examples to concretely and directly illustrate℗¡the correspondence between groups and their Lie algebras. In the second part of the book, the℗¡authors℗¡investigate the basic structure and representation theory of finite dimensional Lie algebras,℗¡such as℗¡the rough structure theory relevant to the theorems of Levi and Malcev, the fine structure of semisimple Lie algebras (root decompositions), and questions related to representation theory. In the third part of the book, the authors turn to global issues, most notably the interplay between differential geometry and Lie theory. Finally, the℗¡fourth part of the book deals with the structure theory of Lie groups, including℗¡some refined applications of the exponential function, various classes of Lie groups, and℗¡structural issues for general Lie groups. To round out the book's content, several appendices appear at the end of this℗¡last part. Containing a wealth of useful information, including new results, Structure and Geometry of Lie Groups provides a unique perspective on the study of Lie groups and℗¡is a valuable addition to the literature. Prerequisites are generally kept to a minimum, and various pedagogical features make it an excellent supplemental text for graduate students. However, the work also contains much that will be of interest to more advanced audiences, and can serve as a useful research reference in the field
21 editions published between 2011 and 2015 in English and held by 121 WorldCat member libraries worldwide
This text is designed as an introduction to Lie groups and their actions on manifolds, one that is accessible both to a broad range of mathematicians and to graduate students.℗¡Building on℗¡the authors' LieGruppen und LieAlgebren textbook from 1991, it℗¡presents the fundamental℗¡ principles of Lie groups℗¡while incorporating the past 20 years of the authors' teaching and research, and giving due emphasis to the role played by differential geometry in the field. The text is entirely self contained,℗¡and provides ample guidance to students with the presence of many exercises and selected hints. The work begins with a study of matrix groups, which serve as examples to concretely and directly illustrate℗¡the correspondence between groups and their Lie algebras. In the second part of the book, the℗¡authors℗¡investigate the basic structure and representation theory of finite dimensional Lie algebras,℗¡such as℗¡the rough structure theory relevant to the theorems of Levi and Malcev, the fine structure of semisimple Lie algebras (root decompositions), and questions related to representation theory. In the third part of the book, the authors turn to global issues, most notably the interplay between differential geometry and Lie theory. Finally, the℗¡fourth part of the book deals with the structure theory of Lie groups, including℗¡some refined applications of the exponential function, various classes of Lie groups, and℗¡structural issues for general Lie groups. To round out the book's content, several appendices appear at the end of this℗¡last part. Containing a wealth of useful information, including new results, Structure and Geometry of Lie Groups provides a unique perspective on the study of Lie groups and℗¡is a valuable addition to the literature. Prerequisites are generally kept to a minimum, and various pedagogical features make it an excellent supplemental text for graduate students. However, the work also contains much that will be of interest to more advanced audiences, and can serve as a useful research reference in the field
LieGruppen und LieAlgebren by
Joachim Hilgert(
Book
)
8 editions published in 1991 in German and held by 75 WorldCat member libraries worldwide
8 editions published in 1991 in German and held by 75 WorldCat member libraries worldwide
Lie theory : Lie algebras and representations by
Jens Carsten Jantzen(
Book
)
8 editions published in 2004 in English and held by 37 WorldCat member libraries worldwide
"Ideal for graduate students and researchers, Lie Theory provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics."Jacket
8 editions published in 2004 in English and held by 37 WorldCat member libraries worldwide
"Ideal for graduate students and researchers, Lie Theory provides a broad, clearly focused examination of semisimple Lie groups and their integral importance to research in many branches of mathematics."Jacket
Universal central extensions of Lie groups by
KarlHermann Neeb(
Book
)
5 editions published in 2001 in English and held by 18 WorldCat member libraries worldwide
5 editions published in 2001 in English and held by 18 WorldCat member libraries worldwide
A topological Maslov index for 3graded Lie groups by
KarlHermann Neeb(
)
5 editions published between 2004 and 2005 in English and held by 15 WorldCat member libraries worldwide
5 editions published between 2004 and 2005 in English and held by 15 WorldCat member libraries worldwide
Lecture at the European School in group theory : infintedimensional groups and their representations by
KarlHermann Neeb(
Book
)
6 editions published between 2000 and 2002 in English and held by 15 WorldCat member libraries worldwide
6 editions published between 2000 and 2002 in English and held by 15 WorldCat member libraries worldwide
Lie algebras and representations by
Jens Carsten Jantzen(
Book
)
1 edition published in 2004 in English and held by 11 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 11 WorldCat member libraries worldwide
Highest weight representations and infinitedimensional Kähler manifolds by
KarlHermann Neeb(
Book
)
4 editions published in 2001 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 2001 in English and held by 9 WorldCat member libraries worldwide
On the cohomology of vector fields on parallelizable manifolds by Yuly Billig(
)
2 editions published in 2007 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 2007 in English and held by 9 WorldCat member libraries worldwide
Lie group structures on groups of smooth and holomorphic maps on noncompact manifolds by
KarlHermann Neeb(
)
2 editions published in 2007 in English and held by 9 WorldCat member libraries worldwide
2 editions published in 2007 in English and held by 9 WorldCat member libraries worldwide
BanachLie quotients, enlargibility, and universal complexifications by
Helge Glöckner(
Book
)
4 editions published in 2001 in English and held by 9 WorldCat member libraries worldwide
4 editions published in 2001 in English and held by 9 WorldCat member libraries worldwide
Central extensions of current groups by Peter Maier(
)
1 edition published in 2002 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 8 WorldCat member libraries worldwide
Semiedges, reflections and coxeter groups by
Ralf Gramlich(
)
1 edition published in 2004 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 8 WorldCat member libraries worldwide
Projective completions of Jordan pairs Part II. Manifold structures and symmetric spaces by
Wolfgang Bertram(
)
1 edition published in 2004 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2004 in English and held by 8 WorldCat member libraries worldwide
Current groups for noncompact manifolds and their central extensions by
KarlHermann Neeb(
)
1 edition published in 2002 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 2002 in English and held by 8 WorldCat member libraries worldwide
Representation theory : current trends and perspectives by
Henning Krause(
Book
)
3 editions published in 2017 in English and held by 1 WorldCat member library worldwide
From April 2009 until March 2016, the German Science Foundation supported generously the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, this is also reflected by the contributions to this volume. Apart from the articles by former postdocs supported by the priority program, the volume contains a number of invited research and survey articles, many of them are extended versions of talks given at the last joint meeting of the priority program in Bad Honnef in March 2015. This volume is covering current research topics from the representation theory of finite groups, of algebraic groups, of Lie superalgebras, of finite dimensional algebras and of infinite dimensional Lie groups. Graduate students and researchers in mathematics interested in representation theory will find this volume inspiring. It contains many stimulating contributions to the development of this broad and extremely diverse subject
3 editions published in 2017 in English and held by 1 WorldCat member library worldwide
From April 2009 until March 2016, the German Science Foundation supported generously the Priority Program SPP 1388 in Representation Theory. The core principles of the projects realized in the framework of the priority program have been categorification and geometrization, this is also reflected by the contributions to this volume. Apart from the articles by former postdocs supported by the priority program, the volume contains a number of invited research and survey articles, many of them are extended versions of talks given at the last joint meeting of the priority program in Bad Honnef in March 2015. This volume is covering current research topics from the representation theory of finite groups, of algebraic groups, of Lie superalgebras, of finite dimensional algebras and of infinite dimensional Lie groups. Graduate students and researchers in mathematics interested in representation theory will find this volume inspiring. It contains many stimulating contributions to the development of this broad and extremely diverse subject
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Related Identities
 Hilgert, Joachim Author
 Pianzola, Arturo 1955 Editor
 Orsted, Bent Editor
 Jantzen, Jens Carsten Author
 Technische Universität Darmstadt Fachbereich Mathematik
 Anker, JeanPhilippe Editor
 Glöckner, Helge Author
 Bertram, Wolfgang Author
 Wagemann, Friedrich
 SpringerLink (Service en ligne)
Associated Subjects
Algebra Algebraic topology Algebras, Linear Categories (Mathematics) Convex functions Geometry Geometry, Algebraic Geometry, Differential Global differential geometry Group theory Harmonic analysis Infinite dimensional Lie algebras Infinite groups Lie algebras Lie groups Linear topological spaces Manifolds (Mathematics) Mathematics Number theory Representations of groups Semigroups Symmetric spaces Topological groups