Quasi-Hopf Algebras: A Categorical Approach (Encyclopedia of Mathematics and its Applications, Series Number 171)

This self-contained book is the first to be dedicated entirely to Drinfeld's quasi-Hopf algebras, from the basics to the state of the art. It includes a detailed introduction to (braided) monoidal categories, the main tool used to study quasi-Hopf algebras. It is ideal for graduate students and researchers in mathematics and mathematical physics. 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. Cover Front Matter Encyclopedia of Mathematics and its Applications Quasi-Hopf Algebras: A Categorical Approach Copyright 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