- 高等教育出版社
- 9787040317091
- 1版
- 47266068-7
- 特殊
- 270
- 理学
- 数学类
- 数学
- 研究生及以上
内容简介
《李理论与表示论（英文版）》包含华东师范大学2009年及2006年“李理论与表示论”研究生暑期学校的4篇讲义。内容包括李超代数表示论的一些新的发 展；有限群概型的几何与组合方面的理论；简约代数群及相关Frobenius核、李型有限群的上同调理论与相互关联；D-模理论在李理论中的应用等。各作 者对相应的专题进行了比较详尽和透彻的叙述，并辅以例子和练习。《李理论与表示论（英文版）》为从事李理论与表示论研究的学生及相关研究人员很好的参考资 料。
目录
目录
Front Matter
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 gl
5 Howe duality for Lie superalgebras of type osp
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-¯nite and tame group schemes
References
Daniel KNakano : 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 ¯nite groups of Lie type
References
Toshiyuki Tanisaki : D-modules and Representation Theory
1 Motivation
2 Basic concepts
3 Derived category
4 Coherent D-modules
5 Regular holonomic D-modules
6 Application to representation theory
References
Front Matter
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 gl
5 Howe duality for Lie superalgebras of type osp
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-¯nite and tame group schemes
References
Daniel KNakano : 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 ¯nite groups of Lie type
References
Toshiyuki Tanisaki : D-modules and Representation Theory
1 Motivation
2 Basic concepts
3 Derived category
4 Coherent D-modules
5 Regular holonomic D-modules
6 Application to representation theory
References
Front Matter
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 gl
5 Howe duality for Lie superalgebras of type osp
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-¯nite and tame group schemes
References
Daniel KNakano : 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 ¯nite groups of Lie type
References
Toshiyuki Tanisaki : D-modules and Representation Theory
1 Motivation
2 Basic concepts
3 Derived category
4 Coherent D-modules
5 Regular holonomic D-modules
6 Application to representation theory
References
Front Matter
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 gl
5 Howe duality for Lie superalgebras of type osp
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-¯nite and tame group schemes
References
Daniel KNakano : 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 ¯nite groups of Lie type
References
Toshiyuki Tanisaki : D-modules and Representation Theory
1 Motivation
2 Basic concepts
3 Derived category
4 Coherent D-modules
5 Regular holonomic D-modules
6 Application to representation theory
References
