Cartan, Elie 18691951
Overview
Works:  323 works in 1,249 publications in 7 languages and 10,152 library holdings 

Genres:  Records and correspondence Bibliography Conference papers and proceedings 
Roles:  Author, Director, Author of introduction, Collector, Honoree, Editor, Other, Contributor, wpr, Publishing director 
Publication Timeline
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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 )
 Selecta; jubilé scientifique by Elie Cartan( 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 )
 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 )
 Anisotropic cosmology in einsteincartan theory by Kwokhing, Albert Kong( Book )
 Élie Cartan et les mathématiques d'aujourd'hui = The mathematical heritage of Elie Cartan : Lyon, 2529 1984( Book )
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Most widely held works by
Elie Cartan
The theory of spinors by
Elie Cartan(
Book
)
68 editions published between 1938 and 2012 in 3 languages and held by 1,025 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
68 editions published between 1938 and 2012 in 3 languages and held by 1,025 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
Geometry of Riemannian spaces by
Elie Cartan(
Book
)
88 editions published between 1921 and 1988 in 4 languages and held by 870 WorldCat member libraries worldwide
88 editions published between 1921 and 1988 in 4 languages and held by 870 WorldCat member libraries worldwide
Leçons sur les invariants intégraux by
Elie Cartan(
Book
)
61 editions published between 1922 and 2005 in 4 languages and held by 431 WorldCat member libraries worldwide
61 editions published between 1922 and 2005 in 4 languages and held by 431 WorldCat member libraries worldwide
Les systèmes differentiels extérieurs et leur applications géométriques by
Elie Cartan(
Book
)
40 editions published between 1945 and 1971 in French and English and held by 355 WorldCat member libraries worldwide
40 editions published between 1945 and 1971 in French and English and held by 355 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
)
46 editions published between 1937 and 1963 in French and Russian and held by 346 WorldCat member libraries worldwide
46 editions published between 1937 and 1963 in French and Russian and held by 346 WorldCat member libraries worldwide
Leçons sur la géométrie projective complexe by
Elie Cartan(
Book
)
33 editions published between 1931 and 1950 in 3 languages and held by 345 WorldCat member libraries worldwide
33 editions published between 1931 and 1950 in 3 languages and held by 345 WorldCat member libraries worldwide
Leçons sur la théorie des espaces à connexion projective by
Elie Cartan(
Book
)
19 editions published between 1937 and 1957 in 3 languages and held by 275 WorldCat member libraries worldwide
19 editions published between 1937 and 1957 in 3 languages and held by 275 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
)
25 editions published in 2001 in 3 languages and held by 267 WorldCat member libraries worldwide
In 1926–27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively 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. In 1960, Sergei P. Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. 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 fiber bundle of a submanifold, etc. 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 also edited the Russian edition
25 editions published in 2001 in 3 languages and held by 267 WorldCat member libraries worldwide
In 1926–27, Cartan gave a series of lectures in which he introduced exterior forms at the very beginning and used extensively 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. In 1960, Sergei P. Finikov translated from French into Russian his notes of these Cartan's lectures and published them as a book entitled Riemannian Geometry in an Orthogonal Frame. 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 fiber bundle of a submanifold, etc. 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 also edited the Russian edition
Œuvres complètes by
Elie Cartan(
Book
)
7 editions published between 1952 and 1953 in French and held by 213 WorldCat member libraries worldwide
7 editions published between 1952 and 1953 in French and held by 213 WorldCat member libraries worldwide
Les espaces de Finsler by
Elie Cartan(
Book
)
15 editions published in 1934 in French and held by 204 WorldCat member libraries worldwide
15 editions published in 1934 in French and held by 204 WorldCat member libraries worldwide
Les espaces métriques fondés la notion d'aire by
Elie Cartan(
Book
)
16 editions published between 1932 and 1971 in French and held by 192 WorldCat member libraries worldwide
16 editions published between 1932 and 1971 in French and held by 192 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
)
23 editions published between 1929 and 1952 in French and Undetermined and held by 175 WorldCat member libraries worldwide
23 editions published between 1929 and 1952 in French and Undetermined and held by 175 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 171 WorldCat member libraries worldwide
21 editions published between 1933 and 1935 in French and held by 171 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 149 WorldCat member libraries worldwide
8 editions published in 1986 in English and held by 149 WorldCat member libraries worldwide
Le parallélisme absolu et la théorie unitaire du champ by
Elie Cartan(
Book
)
13 editions published between 1932 and 1997 in French and held by 140 WorldCat member libraries worldwide
13 editions published between 1932 and 1997 in French and held by 140 WorldCat member libraries worldwide
La géométrie des espaces de Riemann by
Elie Cartan(
Book
)
14 editions published between 1923 and 1951 in French and Undetermined and held by 138 WorldCat member libraries worldwide
14 editions published between 1923 and 1951 in French and Undetermined and held by 138 WorldCat member libraries worldwide
Exposés de géométrie by
Elie Cartan(
Book
)
19 editions published in 1971 in 3 languages and held by 135 WorldCat member libraries worldwide
19 editions published in 1971 in 3 languages and held by 135 WorldCat member libraries worldwide
Selecta; jubilé scientifique by
Elie Cartan(
Book
)
16 editions published in 1939 in French and Undetermined and held by 133 WorldCat member libraries worldwide
16 editions published in 1939 in French and Undetermined and held by 133 WorldCat member libraries worldwide
Sur la structure des groupes de transformations finis et continus by
Elie Cartan(
Book
)
23 editions published between 1894 and 2010 in French and Undetermined and held by 109 WorldCat member libraries worldwide
23 editions published between 1894 and 2010 in French and Undetermined and held by 109 WorldCat member libraries worldwide
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Audience Level
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Related Identities
 Finikov, S. P. (Sergeĭ Pavlovich) 18831964 Other Author
 Mercier, André Annotator Redactor Editor
 Einstein, Albert 18791955
 Debever, Robert Editor
 Streater, R. F. (Raymond Frederick) Author of introduction
 Marty, F. (Frédéric) 1911 Editor
 Vincensini, Paul Félix Other Editor
 Rozenfelʹd, B. A. (Boris Abramovich)
 Akivis, M. A. (Maks Aĭzikovich) Author
 Leroy, Jules 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 Transformation groups 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 franca matematikisto
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 matemàtic francès
Élie Cartan matematician francez
Élie Cartan matemático francés
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
אלי קרטן מתמטיקאי צרפתי
الی کارتان ریاضیدان فرانسوی
إيلي كارتن
إيلي كارتن رياضياتي فرنسي
এলি কারতঁ
এলি কারতঁ ফরাসি গণিতবিদ
엘리 카르탕
エリ・カルタン
カルタン, エリー
埃利·嘉当
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