《李理論與表示論(英文版)》包含華東師范大學(xué)2009年及2006年“李理論與表示論”研究生暑期學(xué)校的4篇講義。內(nèi)容包括李超代數(shù)表示論的一些新的發(fā)展;有限群概型的幾何與組合方面的理論;簡(jiǎn)約代數(shù)群及相關(guān)Frobenius核、李型有限群的上同調(diào)理論與相互關(guān)聯(lián);D-模理論在李理論中的應(yīng)用等。各作者對(duì)相應(yīng)的專(zhuān)題進(jìn)行了比較詳盡和透徹的敘述,并輔以例子和練習(xí)!独罾碚撆c表示論(英文版)》為從事李理論與表示論研究的學(xué)生及相關(guān)研究人員很好的參考資料。
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