Hopf´úÊý¼°ÆäÔÚ»·ÉϵÄ×÷ÓÃ

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£º 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£º the commutative case
4£®3 Trace functions and affine invariants£º 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£º 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¡ã
9£®2 SubHopfalgebras of H¡ã 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