Classical Lie Algebras at Infinity

Preface.- Notation and Terminology. - I. Structure of Locally Reductive Lie Algebras.- 1. Finite-dimensional Lie algebras.- 2. Finite-dimensional Lie superalgebras.- 3. Root-reductive Lie algebras.- 4. Two generalizations.- 5. Splitting Borel subalgebras of sl(infinity), frak o (infinity), sp(infinity) and generalized flags.- 6. General Cartan, Borel and parabolic subalgebras of gl(infinity) and sl(infinity).- II. Modules over Locally Reductive Lie Algebras.- 7. Tensor modules of sl(infinity), frak o(infinity), sp (infinity).- 8. Weight modules.- 9.Generalized Harish-Chandra modules.- III. Geometric aspects. - 10.The Bott-Borel-Weil Theorem.- References.- Index of Notation.- Index.

前言。- 符號和術語。- I. 局部可約李代數的結構。- 1. 有限維李代數。- 2. 有限維李超代數。- 3. 根可約李代數。- 4. 兩個推廣。- 5. sl(infinity), frak o (infinity), sp(infinity)和廣義旗幟的分裂 Borel 子代數。- 6. gl(infinity)和sl(infinity)的一般 Cartan、Borel和拋物線子代數。- II. 局部可約李代數上的模。- 7. sl(infinity), frak o(infinity), sp (infinity)的張量模。- 8. 權重模。- 9. 廣義 Harish-Chandra 模。- III. 幾何方面。- 10. Bott-Borel-Weil 定理。- 參考文獻。- 符號索引。- 索引。