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Hopf代數(shù)及其在環(huán)上的作用
作者：(美)蘇珊·蒙哥馬利
開(kāi)本：
26cm
頁(yè)數(shù)：
238頁(yè)
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Hopf代數(shù)及其在環(huán)上的作用 版權(quán)信息
- ISBN：9787040502312
- 條形碼：9787040502312 ; 978-7-04-050231-2
- 裝幀：一般膠版紙
- 冊(cè)數(shù)：暫無(wú)
- 重量：暫無(wú)
- 所屬分類(lèi)：>
Hopf代數(shù)及其在環(huán)上的作用 內(nèi)容簡(jiǎn)介
近年來(lái)，Hopf代數(shù)出現(xiàn)了許多重大的進(jìn)展。著名的是量子群的引進(jìn)，量子群實(shí)際上就是數(shù)學(xué)物理中的Hopf代數(shù)，現(xiàn)在與許多數(shù)學(xué)領(lǐng)域都有聯(lián)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(guān)于Hopf代數(shù)的一類(lèi)Lagrange定理。關(guān)于Hopf代數(shù)作用方面的工作將早先的群作用、Lie代數(shù)的作用和分次代數(shù)的有關(guān)結(jié)果統(tǒng)一起來(lái)了。 《Hopf代數(shù)及其在環(huán)上的作用（影印版）》將這些新近的發(fā)展按照Hopf代數(shù)的代數(shù)結(jié)構(gòu)和它們的作用及相互作用的觀(guān)點(diǎn)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(diǎn)。書(shū)中用兩章回顧了基本事實(shí)和定義，另外的大部分材料以前并沒(méi)有以書(shū)的形式出現(xiàn)過(guò)！ 禜opf代數(shù)及其在環(huán)上的作用（影印版）》是關(guān)于Hopf代數(shù)的一本優(yōu)秀的研究生教學(xué)參考書(shū)，同時(shí)也是一本量子群的入門(mén)書(shū)。
Hopf代數(shù)及其在環(huán)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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