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Hopf代數及其在環上的作用 版權信息
- ISBN：9787040502312
- 條形碼：9787040502312 ; 978-7-04-050231-2
- 裝幀：一般膠版紙
- 冊數：暫無
- 重量：暫無
- 所屬分類：>
Hopf代數及其在環上的作用 內容簡介
近年來，Hopf代數出現了許多重大的進展。著名的是量子群的引進，量子群實際上就是數學物理中的Hopf代數，現在與許多數學領域都有聯系。除此之外，Kaplansky的許多猜想已得到證明，其中令人驚訝的是關于Hopf代數的一類Lagrange定理。關于Hopf代數作用方面的工作將早先的群作用、Lie代數的作用和分次代數的有關結果統一起來了。 《Hopf代數及其在環上的作用（影印版）》將這些新近的發展按照Hopf代數的代數結構和它們的作用及相互作用的觀點匯攏在一起。量子群是其中重要的例子，而這并非是它們的終點。書中用兩章回顧了基本事實和定義，另外的大部分材料以前并沒有以書的形式出現過。 《Hopf代數及其在環上的作用（影印版）》是關于Hopf代數的一本優秀的研究生教學參考書，同時也是一本量子群的入門書。
Hopf代數及其在環上的作用 目錄
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
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
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