Hopf algebras : an introduction / Sorin Dăscălescu, Constantin Năstăsescu, Șerban Raianu.
Series Monographs and textbooks in pure and applied mathematics ; 235Editor: New York : Marcel Dekker, c2001Descripción: ix, 401 p. ; 24 cmISBN: 0824704819 (alk. paper)Tema(s): Hopf algebrasOtra clasificación: 16W30 Recursos en línea: Publisher descriptionContents Preface iii 1 Algebras and coalgebras [1] 1.1 Basic concepts [1] 1.2 The finite topology [10] 1.3 The dual (co)algebra [16] 1.4 Constructions in the category of coalgebras [23] 1.5 The finite dual of an algebra [33] 1.6 The cofree coalgebra [49] 1.7 Solutions to exercises [55] 2 Comodules [65] 1.1 The category of comodules over a coalgebra [65] 2.2 Rational modules [72] 2.3 Bicomodules and the cotensor product [84] 2.4 Simple comodules and injective comodules [91] 2.5 Some topics on torsion theories on Mc [100] 2.6 Solutions to exercises [110] 3 Special classes of coalgebras [117] 3.1 Cosemisimple coalgebras [117] 3.2 Semiperfect coalgebras [123] 3.3 (Quasi)co-Frobenius and co-Frobenius coalgebras [133] 3.4 Solutions to exercises [140] 4 Bialgebras and Hopf algebras [147] 4.1 Bialgebras [147] 4.2 Hopf algebras [151] 4.3 Examples of Hopf algebras [158] 4.4 Hopf modules [169] 4.5 Solutions to exercises [173] 5 Integrals [181] 5.1 The definition of integrals for a bialgebra [181] 5.2 The connection between integrals and the ideal H*rat [184] 5.3 Finiteness conditions for Hopf algebras with nonzero integrals [189] 5.4 Hie uniqueness of integrals and the bijectivity of the antipode [192] 53 Ideals in Hopf algebras with nonzero integrals [194] 5.6 Hopf algebras constructed by Ore extensions [200] 5.7 Solutions to exercises [221] 6 Actions and coactions of Hopf algebras [233] 6.1 Actions of Hopf algebras on algebras [233] 6.2 Coactions of Hopf algebras on algebras [243] 6.3 The Morita context [251] 6.4 Hopf-Galois extensions [255] 6.5 Application to the duality theorems for co-Frobenius Hopf algebras [267] 6.6 Solutions to exercises [276] 7 Finite dimensional Hopf algebras [289] 7.1 The order of the antipode [289] 7.2 The Nichols-Zoeller Theorem [293] 7.3 Matrix subcoalgebras of Hopf algebras [302] 7.4 Cosemisimplicity, semisimplicity, and the square of the antipode [310] 7.5 Character theory for semisimple Hopf algebras [318] 7.6 The Class Equation and applications [324] 7.7 The Taft-Wilson Theorem [332] 7.8 Pointed Hopf algebras of dimension p" with large coradical [338] 7.9 Pointed Hopf algebras of dimension p3 [343] 7.10 Solutions to exercises [353] A The category theory language [361] A.l Categories, special objects and special morphisms [361] A.2 Functors and functorial morphisms [365] A.3 Abelian categories [367] A.4 Adjoint functors [370] B C-groups and C-cogroups [373] B. l Definitions [373] B.2 General properties of C-groups [376] B.3 Formal groups and affine groups [377] Bibliography [381] Index [399]
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Instituto de Matemática, CONICET-UNS | Libros ordenados por tema | 16 D229 (Browse shelf) | Available | Tapa dura | A-9295 |
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| 16 C678 Skew field constructions / | 16 C678-2 Free rings and their relations / | 16 C978 Representation theory of finite groups and associative algebras / | 16 D229 Hopf algebras : | 16 D242 Modules and rings / | 16 D626 Representations of valued graphs / | 16 D793 Finite dimensional algebras / |
Incluye referencias bibliográficas (p. 381-397) e índice.
Contents --
Preface iii --
1 Algebras and coalgebras [1] --
1.1 Basic concepts [1] --
1.2 The finite topology [10] --
1.3 The dual (co)algebra [16] --
1.4 Constructions in the category of coalgebras [23] --
1.5 The finite dual of an algebra [33] --
1.6 The cofree coalgebra [49] --
1.7 Solutions to exercises [55] --
2 Comodules [65] --
1.1 The category of comodules over a coalgebra [65] --
2.2 Rational modules [72] --
2.3 Bicomodules and the cotensor product [84] --
2.4 Simple comodules and injective comodules [91] --
2.5 Some topics on torsion theories on Mc [100] --
2.6 Solutions to exercises [110] --
3 Special classes of coalgebras [117] --
3.1 Cosemisimple coalgebras [117] --
3.2 Semiperfect coalgebras [123] --
3.3 (Quasi)co-Frobenius and co-Frobenius coalgebras [133] --
3.4 Solutions to exercises [140] --
4 Bialgebras and Hopf algebras [147] --
4.1 Bialgebras [147] --
4.2 Hopf algebras [151] --
4.3 Examples of Hopf algebras [158] --
4.4 Hopf modules [169] --
4.5 Solutions to exercises [173] --
5 Integrals [181] --
5.1 The definition of integrals for a bialgebra [181] --
5.2 The connection between integrals and the ideal H*rat [184] --
5.3 Finiteness conditions for Hopf algebras with nonzero integrals [189] --
5.4 Hie uniqueness of integrals and the bijectivity of the antipode [192] --
53 Ideals in Hopf algebras with nonzero integrals [194] --
5.6 Hopf algebras constructed by Ore extensions [200] --
5.7 Solutions to exercises [221] --
6 Actions and coactions of Hopf algebras [233] --
6.1 Actions of Hopf algebras on algebras [233] --
6.2 Coactions of Hopf algebras on algebras [243] --
6.3 The Morita context [251] --
6.4 Hopf-Galois extensions [255] --
6.5 Application to the duality theorems for co-Frobenius Hopf algebras [267] --
6.6 Solutions to exercises [276] --
7 Finite dimensional Hopf algebras [289] --
7.1 The order of the antipode [289] --
7.2 The Nichols-Zoeller Theorem [293] --
7.3 Matrix subcoalgebras of Hopf algebras [302] --
7.4 Cosemisimplicity, semisimplicity, and the square of the antipode [310] --
7.5 Character theory for semisimple Hopf algebras [318] --
7.6 The Class Equation and applications [324] --
7.7 The Taft-Wilson Theorem [332] --
7.8 Pointed Hopf algebras of dimension p" with --
large coradical [338] --
7.9 Pointed Hopf algebras of dimension p3 [343] --
7.10 Solutions to exercises [353] --
A The category theory language [361] --
A.l Categories, special objects and special morphisms [361] --
A.2 Functors and functorial morphisms [365] --
A.3 Abelian categories [367] --
A.4 Adjoint functors [370] --
B C-groups and C-cogroups [373] --
B. l Definitions [373] --
B.2 General properties of C-groups [376] --
B.3 Formal groups and affine groups [377] --
Bibliography [381] --
Index [399] --
MR, MR1786197
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