Quasi-Hopf Algebras

A Categorical Approach

Daniel Bulacu, Stefaan Caenepeel, Florin Panaite, Freddy Van Oystaeyen

• Publisher: Cambridge University Press
• Year: 2019
• Print ISBN:
  9781108427012
• eBook ISBN:
  9781108632652
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

This is the first book to be dedicated entirely to Drinfeld's quasi-Hopf algebras. Ideal for graduate students and researchers in mathematics and mathematical physics, this treatment is largely self-contained, taking the reader from the basics, with complete proofs, to much more advanced topics, with almost complete proofs. Many of the proofs are based on general categorical results; the same approach can then be used in the study of other Hopf-type algebras, for example Turaev or Zunino Hopf algebras, Hom-Hopf algebras, Hopfish algebras, and in general any algebra for which the category of representations is monoidal. Newcomers to the subject will appreciate the detailed introduction to (braided) monoidal categories, (co)algebras and the other tools they will need in this area. More advanced readers will benefit from having recent research gathered in one place, with open questions to inspire their own research.

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Contents
• Preface
• 1 Monoidal and Braided Categories
• 2 Algebras and Coalgebras in Monoidal Categories
• 3 Quasi-bialgebras and Quasi-Hopf Algebras
• 4 Module (Co)Algebras and (Bi)Comodule Algebras
• 5 Crossed Products
• 6 Quasi-Hopf Bimodule Categories
• 7 Finite-Dimensional Quasi-Hopf Algebras
• 8 Yetter–Drinfeld Module Categories
• 9 Two-sided Two-cosided Hopf Modules
• 10 Quasitriangular Quasi-Hopf Algebras
• 11 Factorizable Quasi-Hopf Algebras
• 12 The Quantum Dimension and Involutory Quasi-Hopf Algebras
• 13 Ribbon Quasi-Hopf Algebras
• Bibliography
• Index