Hopf代数及其在环上的作用（高等教育出版社)
Hopf代数及其在环上的作用
作者：Susan Montgomery[著]
出版社：高等教育出版社出版时间：2018-08-01
开本：26cm
页数：238页
Hopf代数及其在环上的作用 版权信息
- ISBN：9787040502312
- 条形码：9787040502312 ; 978-7-04-050231-2
- 装帧：暂无
- 版次：暂无
- 册数：暂无
- 重量：暂无
- 印刷次数：暂无
Hopf代数及其在环上的作用 内容简介
近年来，Hopf代数出现了许多重大的进展。著名的是量子群的引进，量子群实际上就是数学物理中的Hopf代数，现在与许多数学领域都有联系。除此之外，Kaplansky的许多猜想已得到证明，其中令人惊讶的是关于Hopf代数的一类Lagrange定理。关于Hopf代数作用方面的工作将早先的群作用、Lie代数的作用和分次代数的有关结果统一起来了。 《Hopf代数及其在环上的作用（影印版）》将这些新近的发展按照Hopf代数的代数结构和它们的作用及相互作用的观点汇拢在一起。量子群是其中重要的例子，而这并非是它们的终点。书中用两章回顾了基本事实和定义，另外的大部分材料以前并没有以书的形式出现过。 《Hopf代数及其在环上的作用（影印版）》是关于Hopf代数的一本优秀的研究生教学参考书，同时也是一本量子群的入门书。
Hopf代数及其在环上的作用 目录
Preface
Chapter 1． Definitions and Examples
1．1 Algebras and coalgebras
1．2 Duals of algebras and coalgebras
1．3 Bialgebras
1．4 Convolution and summation notation
1．5 Antipodes and Hopf algebras
1．6 Modules and comodules
1．7 Invariants and coinvariants
1．8 Tensor products of H-modules and H-comodules
1．9 Hopf modules
Chapter 2． Integrals and Semisimplicity
2．1 Integrals
2．2 Maschke’s Theorem
2．3 Commutative semisimple Hopf algebras and restricted enveloping algebras
2．4 Cosemisimplicity and integrals on H
2．5 Kaplansky’s conjecture and the order of the antipode
Chapter 3． Freeness over Subalgebras
3．1 The Nichols-Zoeller Theorem
3．2 Applications： Hopf algebras of prime dimension and semisimple sub Hopfalgebras
3．3 A normal basis for H over K
3．4 The adjoint action， normal subHopfalgebras， and quotients
3．5 Freeness and faithful flatness in the infinite-dimensional case
Chapter 4． Actions of Finite-Dimensional Hopf Algebras and Smash Products
4．1 Module algebras， comodule algebras， and smash products
4．2 Integrality and affine invariants： the commutative case
4．3 Trace functions and affine invariants： the non-commutative case
4．4 Ideals in A#H and A as an All-module
4．5 A Morita context relating A#H and AH
Chapter 5． Coradicals and Filtrations
5．1 Simple subcoalgebras and the coradical
5．2 The coradical filtration
5．3 lnjective coalgebra maps
5．4 The coradical filtration of pointed coalgebras
5．5 Examples： U（g） and Uq（g）
5．6 The structure of pointed cocommutative Hopf algebras
5．7 Semisimple cocommutative connected Hopf algebras
Chapter 6． Inner Actions
6．1 Definitions and examples
6．2 A Skolem-Noether theorem for Hopf algebras
6．3 Maximal inner subcoalgebras
6．4 X-inner actions and extending to quotients
Chapter 7． Crossed products
7．1 Definitions and examples
7．2 Cleft extensions and existence of crossed products
7．3 Inner actions and equivalence of crossed products
7．4 Generalized Maschke theorems and semiprime crossed products
7．5 Twisted H-comodule algebras
Chapter 8． Galois Extensions
8．1 Definition and examples
8．2 The normal basis property and cleft extensions
8．3 Galois extensions for finite-dimensional H
8．4 Normal bases and Hopf algebra quotients
8．5 Relative Hopf modules
Chapter 9． Duality
9．1 H°
9．2 SubHopfalgebras of H° and density
9．3 Classical duality
9．4 Duality for actions
9．5 Duality for graded algebras
Chapter 10． New Constructions from Quantum Groups
10．1 Quasitriangular and ahnost cocommutative Hopf algebras
10．2 Coquasitriangular and almost commutative Hopf algebras
10．3 The Drinfeld double
10．4 Braided monoidal categories
10．SHopf algebras in categories; graded Hopf algebras
10．6 Biproducts and Yetter-Drinfeld modules
Appendix． Some quantum groups
References
Index