Hopf AlgebrasWorld Scientific, 2011 - 584 σελίδες The book provides a detailed account of basic coalgebra and Hopf algebra theory with emphasis on Hopf algebras which are pointed, semisimple, quasitriangular, or are of certain other quantum groups. It is intended to be a graduate text as well as a research monograph. |
Περιεχόμενα
1 Preliminaries | 1 |
2 Coalgebras | 19 |
3 Representations of coalgebras | 77 |
4 The coradical ltration and related structures | 123 |
5 Bialgebras | 165 |
6 The convolution algebra | 203 |
7 Hopf algebras | 211 |
8 Hopf modules and coHopf modules | 259 |
9 Hopf algebras as modules over Hopf subalgebras | 273 |
10 Integrals | 289 |
11 Actions by bialgebras and Hopf algebras | 343 |
12 Quasitriangular bialgebras and Hopf algebras | 387 |
13 The Drinfeld double of a finitedimensional Hopf algebra | 413 |
14 Coquasitriangular bialgebras and Hopf algebras | 447 |
15 Pointed Hopf algebras | 467 |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
a e H algebra over k algebra with antipode basis bialgebra bijective C∗-modules closed subspace coalgebra map coalgebra structure cocommutative cofinite cofinite subspace cofree commutative convolution algebra coproduct coquasitriangular coalgebra coradical Corollary defined Definition denote determined direct sum equation Exercise field filtration finite finite-dimensional Hopf algebra following are equivalent gebra group algebra grouplike element h e H Hint Hom(C Hopf modules Hopf subalgebra ideals of H idempotents implies indecomposable indecomposable components injective hull integral for H inverse isomorphism left coideal left H-module left integral left respectively right Lemma Let H linear map map F morphism non-zero left one-dimensional one-one pointed Hopf algebras Proposition quasitriangular Hopf algebra quotient right C-comodule right coideal satisfies Section semisimple Sh(V simple subcoalgebras sub-bialgebra subalgebra of H subcomodule submodule Suppose that H tensor product Theorem vector space Yang–Baxter equation