Cartan, Elie 18691951
Overview
Works:  304 works in 1,218 publications in 7 languages and 10,103 library holdings 

Genres:  Records and correspondence Bibliography Conference papers and proceedings 
Roles:  Author, Director, Author of introduction, Collector, Honoree, Editor, Other, Contributor 
Classifications:  QA433, 516.83 
Publication Timeline
.
Most widely held works about
Elie Cartan
 Elie CartanAlbert Einstein : letters on absolute parallelism, 19291932 by Elie Cartan( Book )
 Elie Cartan (18691951) by M. A Akivis( Book )
 Notice sur les travaux scientifiques ; suivi de Le parallélisme absolu et la théorie unitaire du champ by Elie Cartan( Book )
 Élie Cartan et les mathématiques d'aujourd'hui, Lyon, 2529 juin 1984 : the mathematical heritage of Elie Cartan( Book )
 Contributions to the study of the equivalence problem of Élie Cartan and its applications to partial and ordinary differential equations by Niky Kamran( Book )
 Jubilé scientifique de M. Élie Cartan célébré a la Sorbonne, le 18 mai, 1939 by Université de Paris( Book )
 Élie Cartan et les mathématiques d'aujourd'hui : Lyon, 2529 juin 1984( Book )
 Elie Cartan et les mathématiques d'aujourd'hui : the mathematical heritage of Elie Cartan, Lyon, 2529 juin 1984 by Lyon> Séminaire Élie Cartan et les Mathématiques d'Aujourd'hui. <1984( Book )
 E. Cartan's theory of exterior differential systems by Robert Hermann( Book )
 The classification of complex simple continuous transitive infinite pseudogroups according to E. Cartan by Masatake Kuranishi( Book )
 Representations of group schemes of Cartan type by William Philip Abrams( )
 Contributo alla teoria delle connessioni by Václav Hlavatý( Book )
 Anisotropic cosmology in einsteincartan theory by Kwokhing, Albert Kong( Book )
 Élie Cartan, 18691951 : hommage de l'Académie de la République Socialiste de Roumanie à l'occasion du centenaire de sa naissance by Elie Cartan( Book )
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Most widely held works by
Elie Cartan
The theory of spinors by
Elie Cartan(
Book
)
45 editions published between 1947 and 2012 in English and Russian and held by 841 WorldCat member libraries worldwide
The French mathematician Élie Cartan (1869{u2013}1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities. The book is divided into two parts. The first is devoted to generalities on the group of rotations in ndimensional space and on the linear representations of groups, and to the theory of spinors in threedimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity. One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value
45 editions published between 1947 and 2012 in English and Russian and held by 841 WorldCat member libraries worldwide
The French mathematician Élie Cartan (1869{u2013}1951) was one of the founders of the modern theory of Lie groups, a subject of central importance in mathematics and also one with many applications. In this volume, he describes the orthogonal groups, either with real or complex parameters including reflections, and also the related groups with indefinite metrics. He develops the theory of spinors (he discovered the general mathematical form of spinors in 1913) systematically by giving a purely geometrical definition of these mathematical entities; this geometrical origin makes it very easy to introduce spinors into Riemannian geometry, and particularly to apply the idea of parallel transport to these geometrical entities. The book is divided into two parts. The first is devoted to generalities on the group of rotations in ndimensional space and on the linear representations of groups, and to the theory of spinors in threedimensional space. Finally, the linear representations of the group of rotations in that space (of particular importance to quantum mechanics) are also examined. The second part is devoted to the theory of spinors in spaces of any number of dimensions, and particularly in the space of special relativity (Minkowski space). While the basic orientation of the book as a whole is mathematical, physicists will be especially interested in the final chapters treating the applications of spinors in the rotation and Lorentz groups. In this connection, Cartan shows how to derive the "Dirac" equation for any group, and extends the equation to general relativity. One of the greatest mathematicians of the 20th century, Cartan made notable contributions in mathematical physics, differential geometry, and group theory. Although a profound theorist, he was able to explain difficult concepts with clarity and simplicity. In this detailed, explicit treatise, mathematicians specializing in quantum mechanics will find his lucid approach a great value
Leçons sur la géométrie des espaces de Riemann by
Elie Cartan(
Book
)
78 editions published between 1921 and 1988 in 4 languages and held by 631 WorldCat member libraries worldwide
78 editions published between 1921 and 1988 in 4 languages and held by 631 WorldCat member libraries worldwide
Leçons sur les invariants intégraux by
Elie Cartan(
Book
)
59 editions published between 1922 and 2005 in 5 languages and held by 427 WorldCat member libraries worldwide
59 editions published between 1922 and 2005 in 5 languages and held by 427 WorldCat member libraries worldwide
Les systèmes differentiels extérieurs et leur applications géométriques by
Elie Cartan(
Book
)
39 editions published between 1945 and 1971 in French and English and held by 350 WorldCat member libraries worldwide
39 editions published between 1945 and 1971 in French and English and held by 350 WorldCat member libraries worldwide
La théorie des groupes finis et continus et la géométrie différentielle, traitées par la méthode du repere mobile. Leçons
professées à la Sorbonne by
Elie Cartan(
Book
)
45 editions published between 1937 and 1963 in 3 languages and held by 346 WorldCat member libraries worldwide
45 editions published between 1937 and 1963 in 3 languages and held by 346 WorldCat member libraries worldwide
Leçons sur la géométrie projective complexe by
Elie Cartan(
Book
)
32 editions published between 1931 and 1950 in 3 languages and held by 338 WorldCat member libraries worldwide
32 editions published between 1931 and 1950 in 3 languages and held by 338 WorldCat member libraries worldwide
Leçons sur la théorie des espaces à connexion projective by
Elie Cartan(
Book
)
20 editions published between 1937 and 1957 in 3 languages and held by 274 WorldCat member libraries worldwide
20 editions published between 1937 and 1957 in 3 languages and held by 274 WorldCat member libraries worldwide
Riemannian geometry in an orthogonal frame : from lectures delivered by Élie Cartan at the Sorbonne in 19261927 by
Elie Cartan(
Book
)
24 editions published in 2001 in 3 languages and held by 263 WorldCat member libraries worldwide
Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 192526. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 192627 were different  he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and nonEuclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition
24 editions published in 2001 in 3 languages and held by 263 WorldCat member libraries worldwide
Elie Cartan's book "Geometry of Riemannian Manifolds" (1928) was one of the best introductions to his methods. It was based on lectures given by the author at the Sorbonne in the academic year 192526. A modernized and extensively augmented edition appeared in 1946 (2nd printing, 1951; 3rd printing, 1988). Cartan's lectures in 192627 were different  he introduced exterior forms at the very beginning and used orthogonal frames throughout to investigate the geometry of Riemannian manifolds. In this course, he solved a series of problems in Euclidean and nonEuclidean spaces, as well as a series of variational problems on geodesics. The lectures were translated into Russian in the book "Riemannian Geometry in an Orthogonal Frame" (1960). This book has many innovations, such as the notion of intrinsic normal differentiation and the Gaussian torsion of a submanifold in a Euclidean multidimensional space or in a space of constant curvature, an affine connection defined in a normal fibre bundle of a submanifold, and so on. This book was available neither in English nor in French. It has now been translated into English by Vladislav V. Goldberg, currently Distinguished Professor of Mathematics at the New Jersey Institute of Technology, USA, who edited the Russian edition
Geometry of Riemannian spaces by
Elie Cartan(
Book
)
8 editions published in 1983 in English and held by 240 WorldCat member libraries worldwide
8 editions published in 1983 in English and held by 240 WorldCat member libraries worldwide
Leçons sur la théorie des spineurs ... by
Elie Cartan(
Book
)
39 editions published between 1938 and 1939 in French and English and held by 237 WorldCat member libraries worldwide
39 editions published between 1938 and 1939 in French and English and held by 237 WorldCat member libraries worldwide
Œuvres complètes by
Elie Cartan(
Book
)
in French and held by 205 WorldCat member libraries worldwide
in French and held by 205 WorldCat member libraries worldwide
Les espaces de Finsler by
Elie Cartan(
Book
)
15 editions published in 1934 in French and held by 201 WorldCat member libraries worldwide
15 editions published in 1934 in French and held by 201 WorldCat member libraries worldwide
La topologie des groupes de Lie by
Elie Cartan(
Book
)
18 editions published in 1936 in French and held by 191 WorldCat member libraries worldwide
18 editions published in 1936 in French and held by 191 WorldCat member libraries worldwide
La théorie des groupes finis et continus et l'analysis situs by
Elie Cartan(
Book
)
21 editions published between 1929 and 1952 in French and Undetermined and held by 172 WorldCat member libraries worldwide
21 editions published between 1929 and 1952 in French and Undetermined and held by 172 WorldCat member libraries worldwide
La méthode du repère mobile, la théorie des groupes continus et les espaces généralisés by
Elie Cartan(
Book
)
21 editions published between 1933 and 1935 in French and held by 170 WorldCat member libraries worldwide
21 editions published between 1933 and 1935 in French and held by 170 WorldCat member libraries worldwide
On manifolds with an affine connection and the theory of general relativity by
Elie Cartan(
Book
)
8 editions published in 1986 in English and held by 150 WorldCat member libraries worldwide
8 editions published in 1986 in English and held by 150 WorldCat member libraries worldwide
Oeuvres complètes by
Elie Cartan(
Book
)
42 editions published between 1955 and 1984 in 3 languages and held by 139 WorldCat member libraries worldwide
42 editions published between 1955 and 1984 in 3 languages and held by 139 WorldCat member libraries worldwide
Le parallélisme absolu et la théorie unitaire du champ by
Elie Cartan(
Book
)
12 editions published between 1932 and 1997 in French and held by 138 WorldCat member libraries worldwide
12 editions published between 1932 and 1997 in French and held by 138 WorldCat member libraries worldwide
La géométrie des espaces de Riemann by
Elie Cartan(
Book
)
13 editions published between 1925 and 1951 in French and Undetermined and held by 136 WorldCat member libraries worldwide
13 editions published between 1925 and 1951 in French and Undetermined and held by 136 WorldCat member libraries worldwide
Exposés de géométrie by
Elie Cartan(
Book
)
18 editions published in 1971 in 3 languages and held by 134 WorldCat member libraries worldwide
18 editions published in 1971 in 3 languages and held by 134 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Finikov, S. P. (Sergeĭ Pavlovich) 18831964 Author
 Mercier, André Redactor Editor
 Einstein, Albert 18791955
 Debever, Robert Editor
 Marty, F. (Frédéric) 1911 Editor
 Vincensini, Paul Félix Other Editor
 Rozenfelʹd, B. A. (Boris Abramovich)
 Akivis, M. A. (Maks Aĭzikovich) Author
 Leroy, Jules Translator
 Ritter, Jim 1943 Translator
Useful Links
Associated Subjects
Algebra Calculus of tensors Cartan, Elie, Celestial mechanics Connections (Mathematics) Continuous groups Cosmology Differential equations Differential equations, Partial Einstein, Albert, Electromagnetism Exterior differential systems France Generalized spaces General relativity (Physics) Geometry Geometry, Differential Geometry, Projective Geometry, Riemannian Gravitation Group schemes (Mathematics) Group theory Invariants Lie algebras Lie groups Manifolds (Mathematics) Mathematical physics Mathematicians Mathematics Metric spaces Multiple integrals Numbers, Complex Physicists Projective differential geometry Pseudogroups Quantum field theory Quantum theory Relativity (Physics) Spinor analysis Topology Transformations, Infinitesimal Transformations (Mathematics) Unified field theories Variables (Mathematics) Vector analysis
Alternative Names
Cartan É.
Cartan É. 18691951
Cartan, E. (Elie), 18691951
Cartan, Élie
Cartan, Élie 18691951
Cartan, Élie J. 18691951
Cartan, Élie Joseph
Cartan, Élie Joseph 18691951
Cartan, M. É. 18691951
Élie Cartan Frans wiskundige
Élie Cartan fransk matematikar
Élie Cartan fransk matematiker
Élie Cartan französischer Mathematiker, der Beiträge zur Theorie der LieGruppen und ihrer Anwendungen lieferte
Élie Cartan French mathematician
Élie Cartan mathématicien français
Élie Joseph Cartan matematico francese
Elie Kartan
Kartan, È.
Kartan, Ėli
Kartan, Ėli 18691951
Елі Жозеф Картан
Картан Э
Картан Э. 18691951
Картан Э.Д
Картан Э.Д. 18691951
Картан, Эли.
Эли Картан
Էլի Ժոսեֆ Կարտան
אלי קרטן
الی کارتان ریاضیدان فرانسوی
إيلي كارتن
এলি কারতঁ
엘리 카르탕
エリ・カルタン
カルタン, エリー
埃利·嘉当
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