Lie, Sophus 18421899
Overview
Works:  376 works in 1,132 publications in 7 languages and 7,722 library holdings 

Genres:  Conference papers and proceedings History Biography Periodicals 
Roles:  Author, Editor, Other, Honoree, Publishing director 
Classifications:  QA385, 512.55 
Publication Timeline
.
Most widely held works about
Sophus Lie
 Felix Klein and Sophus Lie : evolution of the idea of symmetry in the Nineteenth Century by I. M I︠A︡glom( Book )
 The mathematician Sophus Lie : it was the audacity of my thinking by Arild Stubhaug( Book )
 A monograph on Sophus Lie's theory of the phasemanifold with representations in geometry and relativistic mechanics by R. S Capon( Book )
 The Evanston colloquium: lectures on mathematics delivered from Aug. 28 to Sept. 9, 1893 before members of the Congress of mathematics held in connection with the World's fair in Chicago at Northwestern university, Evanston, Ill by Felix Klein( Book )
 Sophus Lie and Felix Klein : the Erlangen program and its impact in mathematics and physics( Book )
 Proceedings by Olav Arnfinn Laudal( Book )
 Conférences sur les mathématiques, faites au Congrès de mathématiques tenu à l'occasion de l'Exposition de Chicago by Felix Klein( Book )
 Sofus Li, 18421899 by Efim Mikhaĭlovich Polishchuk( Book )
 Some applications of group representations by Nolan R Wallach( Visual )
 Sophus Lie : une pensée audacieuse by Arild Stubhaug( Book )
 Sur une généralisation de la transformation de Lie by Herbert Jobin( Book )
 Sophus Lie: ausführliches Verzeichnis seiner Schriften. Mit dem bildnis Sophus Lies in heliogravüre by Friedrich Engel( Book )
 Verzeichniss über den Wissenschaftlichen Nachlass von Sophus Lie by Carl Størmer( Book )
 Verzeichnis über den wissenschaftlichen nachlass von Sophus Lie by Alf Guldberg( Book )
 The theory of perturbations and Lie's theory of contact transformations by Edgar Odell Lovett( )
 Selected papers by Henri Poincaré( )
 Untersuchungen über die im Schlusswort des Lieb'schen Werkes "Geometrie der Berührungstransformationen" angedeuteten Probleme by Philipp Engelhardt( Book )
 Mathematiske Meddelelser af Sophus Lie til Videnskabsselskabet fra Aarene 18691871 by Sophus Lie( Book )
 Sopra una trasformazione classica di Sophus Lie by Enrico Bompiani( Book )
 Study of lie symmetries of the Vaidya equations by Srinath Vadlamani( )
more
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Most widely held works by
Sophus Lie
Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen by
Sophus Lie(
Book
)
35 editions published between 1698 and 2010 in German and English and held by 495 WorldCat member libraries worldwide
35 editions published between 1698 and 2010 in German and English and held by 495 WorldCat member libraries worldwide
Theorie der Transformationsgruppen by
Sophus Lie(
Book
)
64 editions published between 1888 and 2012 in 3 languages and held by 474 WorldCat member libraries worldwide
64 editions published between 1888 and 2012 in 3 languages and held by 474 WorldCat member libraries worldwide
Geometrie der berührungstransformationen by
Sophus Lie(
Book
)
49 editions published between 1896 and 2016 in 3 languages and held by 326 WorldCat member libraries worldwide
49 editions published between 1896 and 2016 in 3 languages and held by 326 WorldCat member libraries worldwide
Lie algebras by
Zhexian Wan(
Book
)
4 editions published in 1975 in English and held by 290 WorldCat member libraries worldwide
Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semisimple Lie algebras and the dependence of structure of semisimple Lie algebras on root systems. The text explains in details the fundamental systems of roots of semi simple Lie algebras and Weyl groups including the properties of the latter. The book addresses the group of automorphisms and the derivation algebra of a Lie algebra and Schur's lemma. The book then shows the characters of irreducible representations of semi simple Lie algebras. This book can be useful for students in advance algebra or who have a background in linear algebra
4 editions published in 1975 in English and held by 290 WorldCat member libraries worldwide
Lie Algebras is based on lectures given by the author at the Institute of Mathematics, Academia Sinica. This book discusses the fundamentals of the Lie algebras theory formulated by S. Lie. The author explains that Lie algebras are algebraic structures employed when one studies Lie groups. The book also explains Engel's theorem, nilpotent linear Lie algebras, as well as the existence of Cartan subalgebras and their conjugacy. The text also addresses the Cartan decompositions and root systems of semisimple Lie algebras and the dependence of structure of semisimple Lie algebras on root systems. The text explains in details the fundamental systems of roots of semi simple Lie algebras and Weyl groups including the properties of the latter. The book addresses the group of automorphisms and the derivation algebra of a Lie algebra and Schur's lemma. The book then shows the characters of irreducible representations of semi simple Lie algebras. This book can be useful for students in advance algebra or who have a background in linear algebra
Sophus Lie's 1880 transformation group paper by
Sophus Lie(
Book
)
13 editions published in 1975 in English and held by 261 WorldCat member libraries worldwide
13 editions published in 1975 in English and held by 261 WorldCat member libraries worldwide
Vorlesungen über differentialgleichungen mit bekannten infinitesimalen transformationen by
Sophus Lie(
Book
)
35 editions published between 1891 and 1980 in German and held by 261 WorldCat member libraries worldwide
35 editions published between 1891 and 1980 in German and held by 261 WorldCat member libraries worldwide
Sophus Lie's 1884 differential invariant paper by
Sophus Lie(
Book
)
9 editions published in 1976 in English and held by 233 WorldCat member libraries worldwide
9 editions published in 1976 in English and held by 233 WorldCat member libraries worldwide
DifferentialGleichungen by
Sophus Lie(
Book
)
21 editions published between 1891 and 2004 in 3 languages and held by 205 WorldCat member libraries worldwide
21 editions published between 1891 and 2004 in 3 languages and held by 205 WorldCat member libraries worldwide
Oeuvres complètes de Niels Henrik Abel by
Niels Henrik Abel(
Book
)
49 editions published between 1881 and 2014 in 3 languages and held by 184 WorldCat member libraries worldwide
Niels Henrik Abel (1802–29) was one of the most prominent mathematicians in the first half of the nineteenth century. His pioneering work in diverse areas such as algebra, analysis, geometry and mechanics has made the adjective 'abelian' a commonplace in mathematical writing. These collected works, first published in two volumes in 1881 after careful preparation by the mathematicians Ludwig Sylow (1832–1918) and Sophus Lie (1842–99), contain some of the pillars of mathematical history. Volume 1 includes perhaps the most famous of Abel's results, namely his proof of the 'impossibility theorem', which states that the general fifthdegree polynomial is unsolvable by algebraic means. Also included in this volume is Abel's 'Paris memoir', which contains his many fundamental results on transcendental functions  in particular on elliptic integrals, elliptic functions, and what are known today as abelian integrals
49 editions published between 1881 and 2014 in 3 languages and held by 184 WorldCat member libraries worldwide
Niels Henrik Abel (1802–29) was one of the most prominent mathematicians in the first half of the nineteenth century. His pioneering work in diverse areas such as algebra, analysis, geometry and mechanics has made the adjective 'abelian' a commonplace in mathematical writing. These collected works, first published in two volumes in 1881 after careful preparation by the mathematicians Ludwig Sylow (1832–1918) and Sophus Lie (1842–99), contain some of the pillars of mathematical history. Volume 1 includes perhaps the most famous of Abel's results, namely his proof of the 'impossibility theorem', which states that the general fifthdegree polynomial is unsolvable by algebraic means. Also included in this volume is Abel's 'Paris memoir', which contains his many fundamental results on transcendental functions  in particular on elliptic integrals, elliptic functions, and what are known today as abelian integrals
Theorie der Transformationsgruppen by
Sophus Lie(
Book
)
40 editions published between 1888 and 1980 in German and held by 144 WorldCat member libraries worldwide
40 editions published between 1888 and 1980 in German and held by 144 WorldCat member libraries worldwide
Séminaire "Sophus Lie" : [exposés] by Séminaire "Sophus Lie."(
)
in French and held by 112 WorldCat member libraries worldwide
in French and held by 112 WorldCat member libraries worldwide
Œuvres complètes by
Niels Henrik Abel(
Book
)
2 editions published in 1965 in French and held by 110 WorldCat member libraries worldwide
2 editions published in 1965 in French and held by 110 WorldCat member libraries worldwide
Gesammelte Abhandlungen by
Sophus Lie(
Book
)
26 editions published between 1922 and 1973 in 3 languages and held by 98 WorldCat member libraries worldwide
26 editions published between 1922 and 1973 in 3 languages and held by 98 WorldCat member libraries worldwide
Über die Grundlagen der Geometrie by
Sophus Lie(
Book
)
14 editions published in 1967 in German and held by 76 WorldCat member libraries worldwide
14 editions published in 1967 in German and held by 76 WorldCat member libraries worldwide
Beiträge zur Theorie der Differentialinvarianten by
Sophus Lie(
Book
)
6 editions published between 1992 and 1993 in German and held by 63 WorldCat member libraries worldwide
6 editions published between 1992 and 1993 in German and held by 63 WorldCat member libraries worldwide
Über Integralinvarianten und Differentialgleichungen by
Sophus Lie(
Book
)
23 editions published between 1902 and 2008 in German and English and held by 58 WorldCat member libraries worldwide
23 editions published between 1902 and 2008 in German and English and held by 58 WorldCat member libraries worldwide
Untersuchungen über unendliche continuirliche Gruppen by
Sophus Lie(
Book
)
8 editions published between 1893 and 1895 in German and held by 57 WorldCat member libraries worldwide
8 editions published between 1893 and 1895 in German and held by 57 WorldCat member libraries worldwide
Classification der flächen nach der transformationsgruppe ihrer geodätischen curven by
Sophus Lie(
Book
)
12 editions published in 1879 in German and Norwegian and held by 54 WorldCat member libraries worldwide
12 editions published in 1879 in German and Norwegian and held by 54 WorldCat member libraries worldwide
Theory of transformation groups I : General properties of continuous transformation groups ; a contemporary approach and translation by
Sophus Lie(
Book
)
18 editions published between 2015 and 2016 in English and German and held by 48 WorldCat member libraries worldwide
This modern translation of Sophus Lie's and Friedrich Engel's ℓ́ℓTheorie der Transformationsgruppen Band Iℓ́ℓ will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations, and also in physics, for example in general relativity. This volume℗ℓis of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry
18 editions published between 2015 and 2016 in English and German and held by 48 WorldCat member libraries worldwide
This modern translation of Sophus Lie's and Friedrich Engel's ℓ́ℓTheorie der Transformationsgruppen Band Iℓ́ℓ will allow readers to discover the striking conceptual clarity and remarkably systematic organizational thought of the original German text. Volume I presents a comprehensive introduction to the theory and is mainly directed towards the generalization of ideas drawn from the study of examples. The major part of the present volume offers an extremely clear translation of the lucid original. The first four chapters provide not only a translation, but also a contemporary approach, which will help present day readers to familiarize themselves with the concepts at the heart of the subject. The editor's main objective was to encourage a renewed interest in the detailed classification of Lie algebras in dimensions 1, 2 and 3, and to offer access to Sophus Lie's monumental Galois theory of continuous transformation groups, established at the end of the 19th Century. Lie groups are widespread in mathematics, playing a role in representation theory, algebraic geometry, Galois theory, the theory of partial differential equations, and also in physics, for example in general relativity. This volume℗ℓis of interest to researchers in Lie theory and exterior differential systems and also to historians of mathematics. The prerequisites are a basic knowledge of differential calculus, ordinary differential equations and differential geometry
Om Poncelet's betydning for geometrien. Et bidrag til de moderngeometriske ideers udviklingshistorie by
Elling Holst(
Book
)
9 editions published between 1878 and 2017 in Norwegian and Danish and held by 47 WorldCat member libraries worldwide
9 editions published between 1878 and 2017 in Norwegian and Danish and held by 47 WorldCat member libraries worldwide
more
fewer
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Related Identities
 Scheffers, Georg 18661945 Other Author Editor Creator
 Engel, Friedrich 18611941 Other Editor Publishing director Author Contributor Creator
 Klein, Felix 18491925 Author
 Abel, Niels Henrik 18021829 Author
 Stubhaug, Arild 1948 Author
 Sylow, Ludvig 18321918 Author Editor
 Hermann, Robert 1931 Author of introduction Author Editor
 Яглом, И. М (Исаак Моисеевич) 19211988 Author
 Shenitzer, Abe
 Grant, Hardy
Useful Links
Associated Subjects
Algebra, Abstract Clebsch, Alfred, Congresses and conventions Contact transformations Continuous groups Craig, Thomas, Curves Darwin, George Howard,Sir, Differential equations Differential invariants Elliptic functions Equations Functions Functions, Abelian Geometric group theory Geometry Geometry, Differential Geometry, NonEuclidean Geometry, Projective GeometryFoundations Group theory Hermite, Charles, Hertz, Heinrich, Integrals Kelvin, William Thomson,Baron, Klein, Felix, Lie, Sophus, Lie algebras Lie groups Mathematical physics Mathematicians Mathematics Mathematics, German MathematicsStudy and teaching Minimal surfaces MittagLeffler, Magnus Gustaf, Norway Perturbation (Mathematics) PhysicsPhilosophy Poncelet,M.(Jean Victor), Quantum theory Representations of groups Series Surfaces Symmetry Topology Transformation groups Transformations, Infinitesimal Transformations (Mathematics) Universität Göttingen
Alternative Names
Li, Sofus.
Li Sofus 18421899
Lie, Marius S. 18421899
Lie, Marius Sophus
Lie Marius Sophus 18421899
Lie, S.
Lie, Sophus
Lie, Sophus Marius.
Marius Sophus Lie matematyk norweski
Sophus Lie matemàtic noruec
Sophus Lie matematician norvegian
Sophus Lie matemático noruego
Sophus Lie matemático noruegués
Sophus Lie matematico norvegese
Sophus Lie mathématicien norvégien
Sophus Lie Noors wiskundige
Sophus Lie norsk professor och matematiker
Sophus Lie norsk professor og matematikar
Sophus Lie norsk professor og matematiker
Sophus Lie norvég matematikus
Sophus Lie norvega matematikisto
Sophus Lie Norwegian mathematician
Sophus Lie norwegischer Mathematiker
Ли, Мариус Софус
Ли Софус Мариус
Софус Ли
Софус Ли норвежский математик
Софус Ли норвешки математичар
Софус Лі
סופוס לי
סופוס לי מתמטיקאי נורווגי
سوفوس لي
سوفوس لي رياضياتي نرويجي
سوفوس لی ریاضیدان نروژی
소푸스 리
ソフス・リー
リー, ソーフス
索菲斯·李
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