WorldCat Identities

Lie, Sophus 1842-1899

Overview
Works: 358 works in 1,005 publications in 8 languages and 7,443 library holdings
Genres: Conference papers and proceedings  History  Biography  Periodicals 
Roles: Author, Editor, Other, Publishing director
Classifications: QA385, 512.55
Publication Timeline
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Most widely held works about Sophus Lie
 
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Most widely held works by Sophus Lie
Theorie der Transformationsgruppen by Sophus Lie( Book )

62 editions published between 1876 and 2015 in 4 languages and held by 491 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
Vorlesungen über continuierliche Gruppen mit geometrischen und anderen Anwendungen by Sophus Lie( Book )

21 editions published between 1893 and 1980 in German and held by 475 WorldCat member libraries worldwide

Gesammelte Abhandlungen by Sophus Lie( Book )

127 editions published between 1922 and 1973 in 3 languages and held by 385 WorldCat member libraries worldwide

Lie algebras by Zhexian Wan( Book )

5 editions published between 1964 and 1975 in English and Chinese and held by 301 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 semi-simple Lie algebras and the dependence of structure of semi-simple 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
Geometrie der berührungstransformationen by Sophus Lie( Book )

31 editions published between 1896 and 2005 in German and English and held by 274 WorldCat member libraries worldwide

Vorlesungen über differentialgleichungen mit bekannten infinitesimalen transformationen by Sophus Lie( Book )

34 editions published between 1891 and 1980 in German and held by 266 WorldCat member libraries worldwide

Sophus Lie's 1880 transformation group paper by Sophus Lie( Book )

5 editions published in 1975 in English and held by 243 WorldCat member libraries worldwide

Sophus Lie's 1884 differential invariant paper by Sophus Lie( Book )

6 editions published in 1976 in English and held by 229 WorldCat member libraries worldwide

Differential-Gleichungen by Sophus Lie( Book )

13 editions published between 1891 and 2004 in German and English and held by 177 WorldCat member libraries worldwide

Oeuvres complètes de Niels Henrik Abel by Niels Henrik Abel( Book )

39 editions published between 1881 and 2014 in 3 languages and held by 177 WorldCat member libraries worldwide

Séminaire "Sophus Lie" : [exposés] by Séminaire "Sophus Lie."( )

in French and held by 115 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

Gesammelte Abhandlungen by Sophus Lie( Book )

42 editions published between 1922 and 1973 in 3 languages and held by 94 WorldCat member libraries worldwide

Theorie der Transformationsgruppen by Sophus Lie( Book )

19 editions published between 1890 and 1980 in German and Undetermined and held by 83 WorldCat member libraries worldwide

Über die Grundlagen der Geometrie by Sophus Lie( Book )

12 editions published in 1967 in German and held by 74 WorldCat member libraries worldwide

Theorie der Transformationsgruppen by Sophus Lie( Book )

18 editions published between 1893 and 1970 in German and Undetermined and held by 67 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

Untersuchungen über unendliche continuirliche Gruppen by Sophus Lie( Book )

8 editions published between 1893 and 1895 in German and held by 56 WorldCat member libraries worldwide

Über Integralinvarianten und Differentialgleichungen by Sophus Lie( Book )

15 editions published between 1902 and 2008 in German and English and held by 51 WorldCat member libraries worldwide

Om Poncelet's betydning for geometrien. Et bidrag til de moderngeometriske ideers udviklingshistorie by Elling Holst( Book )

7 editions published in 1878 in Norwegian and Danish and held by 47 WorldCat member libraries worldwide

 
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Differential-Gleichungen
Alternative Names
Li, Sofus.

Li Sofus 1842-1899

Lie, Marius S. 1842-1899

Lie, Marius Sophus

Lie Marius Sophus 1842-1899

Lie, S.

Lie, Sophus

Lie, Sophus Marius.

Marius Sophus Lie matematyk norweski

Sophus Lie matemático noruego

Sophus Lie matematico norvegese

Sophus Lie mathématicien

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 Norwegian mathematician

Sophus Lie norwegischer Mathematiker

Ли, Софус

Софус Ли

Софус Ли норвежский математик

Софус Ли норвешки математичар

Софус Лі

סופוס לי

سوفوس لي

سوفوس لی ریاضی‌دان نروژی

소푸스 리

ソフス・リー

リー, ソーフス

索菲斯·李

Languages
German (369)

English (64)

French (39)

Norwegian (18)

Russian (4)

Chinese (2)

Danish (2)

Italian (1)

Covers
Geometries, groups and algebras in the nineteenth century : a historySophus Lie : une pensée audacieuse