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Hopf代数及其在环上的作用PDF|Epub|txt|kindle电子书版本网盘下载
- （美）苏珊·蒙哥马利（Susan Montgomery）著 著
- 出版社： 北京：高等教育出版社
- ISBN：9787040502312
- 出版时间：2018
- 标注页数：238页
- 文件大小：27MB
- 文件页数：249页
- 主题词：hopf代数－英文
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图书目录
Chapter 1．Definitions and Examples1
1.1 Algebras and coalgebras1
1.2 Duals of algebras and coalgebras2
1.3 Bialgebras3
1.4 Convolution and summation notation6
1.5 Antipodes and Hopf algebras7
1.6 Modules and comodules10
1.7 Invariants and coinvariants13
1.8 Tensor products of H-modules and H-comodules14
1.9 Hopf modules14
Chapter 2．Integrals and Semisimplicity17
2.1 Integrals17
2.2 Maschke’s Theorem20
2.3 Commutative semisimple Hopf algebras and restricted enveloping algebras22
2.4 Cosemisimplicity and integrals on H25
2.5 Kaplansky’s conjecture and the order of the antipode27
Chapter 3．Freeness over Subalgebras28
3.1 The Nichols-Zoeller Theorem28
3.2 Applications:Hopf algebras of prime dimension and semisimple subHopfalgebras31
3.3 A normal basis for H over K32
3.4 The adjoint action,normal subHopfalgebras,and quotients33
3.5 Freeness and faithful flatness in the infinite-dimensional case37
Chapter 4．Actions of Finite-Dimensional Hopf Algebras and Smash Products40
4.1 Module algebras,comodule algebras,and smash products40
4.2 Integrality and affine invariants:the commutative case43
4.3 Trace functions and affine invariants:the non-commutative case45
4.4 Ideals in A#H and A as an AH module48
4.5 A Morita context relating A#H and AH52
Chapter 5．Coradicals and Filtrations56
5.1 Simple subcoalgebras and the coradical56
5.2 The coradical filtration60
5.3 Injecti ve coalgebra maps65
5.4 The coradical filtration of pointed coalgebras67
5.5 Examples:U（g）and Uq（g）73
5.6 The structure of pointed cocommutative Hopf algebras76
5.7 Semisimple cocommutative connected Hopf algebras83
Chapter 6．Inner Actions87
6.1 Definitions and examples87
6.2 A Skolem-Noether theorem for Hopf algebras89
6.3 Maximal inner subcoalgebras92
6.4 X-inner actions and extending to quotients96
Chapter 7．Crossed products101
7.1 Definitions and examples101
7.2 Cleft extensions and existence of crossed products105
7.3 Inner actions and equivalence of crossed products112
7.4 Generalized Maschke theorems and semiprime crossed products116
7.5 Twisted H-comodule algebras121
Chapter 8．Galois Extensions123
8.1 Definition and examples123
8.2 The normal basis property and cleft extensions128
8.3 Galois extensions for finite-dimensional H131
8.4 Normal bases and Hopf algebra quotients139
8.5 Relative Hopf modules144
Chapter 9．Duality149
9.1 H°149
9.2 SubHopfalgebras of H°and density153
9.3 Classical duality159
9.4 Duality for actions161
9.5 Duality for graded algebras172
Chapter 10．New Constructions from Quantum Groups178
10.1 Quasitriangular and almost cocommutative Hopf algebras178
10.2 Coquasitriangular and almost commutative Hopf algebras184
10.3 The Drinfeld double187
10.4 Braided monoidal categories197
10.5 Hopf algebras in categories;graded Hopf algebras203
10.6 Biproducts and Yetter-Drinfeld modules207
Appendix．Some quantum groups217
References223
Index235