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Hopf Algebras and Generalizations
Edited by: Louis H. Kauffman and David E. Radford, University of Illinois at Chicago, IL, and Fernando J. O. Souza, Universidade Federal de Pernambuco, Recife, PE, Brazil

Contemporary Mathematics
2007; 174 pp; softcover
Volume: 441
ISBN-10: 0-8218-3820-2
ISBN-13: 978-0-8218-3820-4
List Price: US$61
Member Price: US$48.80
Order Code: CONM/441
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Hopf algebras have proved to be very interesting structures with deep connections to various areas of mathematics, particularly through quantum groups. Indeed, the study of Hopf algebras, their representations, their generalizations, and the categories related to all these objects has an interdisciplinary nature. It finds methods, relationships, motivations and applications throughout algebra, category theory, topology, geometry, quantum field theory, quantum gravity, and also combinatorics, logic, and theoretical computer science.

This volume portrays the vitality of contemporary research in Hopf algebras. Altogether, the articles in the volume explore essential aspects of Hopf algebras and some of their best-known generalizations by means of a variety of approaches and perspectives. They make use of quite different techniques that are already consolidated in the area of quantum algebra. This volume demonstrates the diversity and richness of its subject. Most of its papers introduce the reader to their respective contexts and structures through very expository preliminary sections.


Graduate students and research mathematicians interested in Hopf algebras, their applications and generalizations.

Table of Contents

  • B. Day, E. Panchadcharam, and R. Street -- Lax braidings and the Lax centre
  • G. Karaali -- Dynamical quantum groups-The super story
  • Y. Kashina -- Groups of grouplike elements of a semisimple Hopf algebra and its dual
  • S.-H. Ng and P. Schauenburg -- Higher Frobenius-Schur indicators for pivotal categories
  • F. Panaite -- Doubles of (quasi) Hopf algebras and some examples of quantum groupoids and vertex groups related to them
  • P. Schauenburg -- Central braided Hopf algebras
  • M. D. Staic -- A note on anti-Yetter-Drinfeld modules
  • M. Takeuchi -- Representations of the Hopf algebra \(U(n)\)
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