Hopf Algebras and Their Actions on Rings, Τεύχος 82American Mathematical Soc., 28 Οκτ 1993 - 238 σελίδες The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups. |
Περιεχόμενα
Integrals and Semisimplicity | 17 |
Freeness over Subalgebras | 28 |
Actions of FiniteDimensional Hopf Algebras | 40 |
Coradicals and Filtrations | 56 |
Inner Actions | 87 |
Crossed products | 101 |
Galois Extensions | 123 |
Duality | 149 |
New Constructions from Quantum Groups | 178 |
Appendix Some quantum groups | 217 |
References | 223 |
| 235 | |
Άλλες εκδόσεις - Προβολή όλων
Hopf Algebras and Their Actions on Rings, Τόμος 82 Susan Montgomery Δεν υπάρχει διαθέσιμη προεπισκόπηση - 1993 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A C B A#UH action of H adjoint action affine algebra H algebra map antipode Artinian assume automorphisms bialgebra bijective braided monoidal category choose coalgebra cocommutative cocycle coideal commutative comodule consider coradical COROLLARY cosemisimple crossed product define definition dual enveloping algebras equivalent EXAMPLE fact field filtration finite group finite-dimensional finite-dimensional Hopf algebra first follows G-graded Galois extensions given gives graded graded algebras group actions group algebra group G group-like elements h E H H I kG H I U(g H is cocommutative H is finite-dimensional H-comodule map H-module algebra Hopf modules injective inner invertible irreducible isomorphism k-algebra left H-module LEMMA Let g Lie algebra Math matrix monoidal category morphism multiplication notation Note PROOF prove quantum groups quasitriangular quasitriangular Hopf algebras quotient recall result right H-comodule right K-module ring satisfies semiprime semisimple simple subcoalgebra smash product structure subspace suffices to show surjective