Essays in the History of Lie Groups and Algebraic Groups 0-8218-0288-7, 9780821802885

Table of contents :
Content: Lie's theory --
Lie algebras --
Globalizations --
Full reducibility and invariants for SL[subscript 2] (C) --
Full reducibility, 1890-96 --
Averaging. The invariant theorem --
Algebraic proofs of full reducibility --
Appendix: More on some proofs of full reducibility --
Hermann Weyl and Lie groups --
First contacts with Lie groups --
Representations of semisimple Lie groups and Lie algebras --
Impact on E. Cartan --
The Peter-Weyl theorem. Harmonic analysis --
Group theory and quantum mechanics --
Representations and invariants of classical groups --
Two later developments --
Elie Cartan, symmetric spaces and Lie groups --
Building up the theory --
The spaces [varepsilon]. Local theory --
Spaces [varepsilon] and semisimple groups. Global theory --
An exposition of Lie group theory from the global point of view --
Further developments --
Complete orthogonal systems on homogeneous spaces of compact Lie groups --
Differential forms and algebraic topology --
Bounded symmetric domains --
Linear algebraic groups in the 19th Century --
S. Lie, E. Study, and projective representations --
E. Study, Gordan series and linear representations of SL[subscript 3] --
Emile Picard --
Ludwig Maurer --
Elie Cartan --
Karl Carda --
Linear algebraic groups in the 20th Century --
Linear algebraic groups in characteristic zero. Replicas --
Groups over algebraically closed ground fields I --
Groups over an algebraically closed ground field II --
Rationality properties --
Algebraic groups and geometry. Tits systems and Tits buildings. Abstract automorphisms --
Merger --
The work of Chevalley in Lie groups and algebraic groups --
Lie groups, 1941-1946 --
Linear algebraic groups, 1943-1951 --
Lie groups, 1948-1955 --
Algebraic groups, 1955-1961 --
Algebraic groups and Galois theory in the work of Ellis R. Kolchin --
The Picard-Vessiot theory --
Linear algebraic groups --
Generalization of the Picard-Vessiot theory --
Galois theory of the strongly normal extensions --
Foundational work on algebraic sets and groups.

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