Hopf algebras and their actions on rings
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Bibliographic Information
Hopf algebras and their actions on rings
(Regional conference series in mathematics, no. 82)
American Mathematical Society, c1993
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"Expanded version of ten lectures given at the CBMS Conference on Hopf Algebras and Their Actions on Rings, which took place at DePaul University in Chicago, August 10-14, 1992" -- Pref
Includes bibliographical references and index
Description and Table of Contents
Description
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.
Table of Contents
Definitions and examples Integrals and semisimplicity Freeness over subalgebras Action of finite-dimensional Hopf algebras and smash products Coradicals and filtrations Inner actions Crossed products Galois extensions Duality New constructions from quantum groups Some quantum groups.
by "Nielsen BookData"