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Hopf algebras : an introduction / Sorin Dăscălescu, Constantin Năstăsescu, Șerban Raianu.

By: Dăscălescu, Sorin.
Contributor(s): Năstăsescu, C. (Constantin), 1943- | Raianu, Șerban.
Material type: materialTypeLabelBookSeries: Monographs and textbooks in pure and applied mathematics ; 235. Publisher: New York : Marcel Dekker, c2001Description: ix, 401 p. ; 24 cm.ISBN: 0824704819 (alk. paper).Subject(s): Hopf algebrasOther classification: 16W30 Online resources: Publisher description
Contents:
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] --
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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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