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Cambridge University Press
Online publication date:
February 2019
Print publication year:
Online ISBN:

Book description

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.


'This book serves as a thorough reference source for topics related to the algebraic structure of quasi-Hopf algebras, their representations, and many key examples. By using the language of category theory throughout, this book presents its material very abstractly but in a way that allows results from the study of Hopf algebras to generalize to quasi-Hopf algebras.'

Kevin Gerstle Source: MAA Reviews

‘The aim of this book is the development of the theory of quasi-Hopf algebras, mainly with algebraic means, and widely using the language of monoidal categories. It is, as far as possible, self-contained.’

Loïc Foissy Source: zbMATH

'… the book is an excellent reference both as an introduction to the subject and as a source for research in fields related to tensor categories.'

Sonia Natale Source: MathSciNet

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