Essays in the history of Lie groups and algebraic groups / Armand Borel.

Format:

• Book

Author/Creator:

• Borel, Armand.

Series:

• History of mathematics 0899-2428 ; v. 21.
• History of mathematics, 0899-2428 ; v. 21

Language:

English

Subjects (All):

• Lie groups--History.
• Linear algebraic groups--History.
• Linear algebraic groups.
• History.
• Lie groups.

Physical Description:

xiii, 184 pages : portraits ; 26 cm.

Place of Publication:

Providence, R.I. : American Mathematical Society ; [London] : London Mathematical Society, [2001]

Contents:

• 1. Lie's theory 1
• 2. Lie algebras 5
• 3. Globalizations 6
• Chapter II. Full Reducibility and Invariants for SL[subscript 2] (C) 9
• 1. Full reducibility, 1890-96 9
• 2. Averaging. The invariant theorem 11
• 3. Algebraic proofs of full reducibility 16
• 4. Appendix: More on some proofs of full reducibility 18
• Chapter III. Hermann Weyl and Lie Groups 29
• 1. First contacts with Lie groups 29
• 2. Representations of semisimple Lie groups and Lie algebras 31
• 3. Impact on E. Cartan 35
• 4. The Peter-Weyl theorem. Harmonic analysis 37
• 5. Group theory and quantum mechanics 38
• 6. Representations and invariants of classical groups 40
• 7. Two later developments 44
• Chapter IV. Elie Cartan, Symmetric Spaces and Lie Groups 59
• A. Building Up the Theory 60
• 1. The spaces [varepsilon]. Local theory 60
• 2. Spaces [varepsilon] and seminismple groups. Global theory 64
• 3. An exposition of Lie group theory from the global point of view 79
• B. Further Developments 80
• 4. Complete orthogonal systems on homogeneous spaces of compact Lie groups 80
• 5. Differential forms and algebraic topology 84
• 6. Bounded symmetric domains 88
• Chapter V. Linear Algebraic Groups in the 19th Century 93
• 1. S. Lie, E. Study, and projective representations 93
• 2. E. Study, Gordan series and linear representations of SL[subscript 3] 97
• 3. Emile Picard 99
• 4. Ludwig Maurer 102
• 5. Elie Cartan 114
• 6. Karl Carda 115
• Chapter VI. Linear Algebraic Groups in the 20th Century 119
• 1. Linear algebraic groups in characteristic zero. Replicas 119
• 2. Groups over algebraically closed ground fields I 119
• 3. Groups over an algebraically closed ground field II 124
• 4. Rationality properties 126
• 5. Algebraic groups and geometry. Tits systems and Tits buildings 131
• 6. Abstract automorphisms 134
• 7. Merger 142
• Chapter VII. The Work of Chevalley in Lie Groups and Algebraic Groups 147
• 1. Lie groups, 1941-1946 147
• 2. Linear algebraic groups, 1943-1951 150
• 3. Lie groups, 1948-1955 152
• 4. Linear algebraic groups, 1954 155
• 5. Algebraic groups, 1955-1961 156
• Chapter VIII. Algebraic Groups and Galois Theory in the Work of Ellis R. Kolchin 165
• 1. The Picard-Vessiot theory 165
• 2. Linear algebraic groups 169
• 3. Generalization of the Picard-Vessiot theory 170
• 4. Galois theory of strongly normal extensions 173
• 5. Foundational work on algebraic sets and groups 176.

Notes:

Includes bibliographical references and indexes.

ISBN:

0821802887

OCLC:

45757804