內容簡介
《李理論與錶示論(英文版)》包含華東師範大學2009年及2006年“李理論與錶示論”研究生暑期學校的4篇講義。內容包括李超代數錶示論的一些新的發展;有限群概型的幾何與組閤方麵的理論;簡約代數群及相關Frobenius核、李型有限群的上同調理論與相互關聯;D-模理論在李理論中的應用等。各作者對相應的專題進行瞭比較詳盡和透徹的敘述,並輔以例子和練習。《李理論與錶示論(英文版)》為從事李理論與錶示論研究的學生及相關研究人員很好的參考資料。
目錄
Shun-Jen Cheng and Weiqiang Wang: Dualities for Lie Superalgebras
0 Introduction
1 Lie superalgebra ABC
2 Finite-dimensional modules of Lie superalgebras
3 Schur-Sergeev duality
4 Howe duality for Lie superalgebras of type
5 Howe duality for Lie superalgebras of type
6 Super duality
References
Rolf Farnsteiner: Combinatorial and Geometric Aspects of the
Representation Theory of Finite Group Schemes
0 Introduction
1 Finite group schemes
2 Complexity and representation type
3 Support varieties and support spaces
4 Varieties of tori
5 Quivers and path algebras
6 Representation-finite and tame group schemes
References
Daniel K. Nakano : Cohomology of Algebraic Groups, Finite Groups, and Lie Algebras: Interactions and Connections
1 Overview
2 Representation theory
3 Homological algebra
4 Relating support varieties
5 Relating cohomology
6 Computing cohomology for finite groups of Lie type
References
Toshiyuki Tanisaki: D-modules and Representation Theory
1 Motivation
2 Basic concepts
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