Quasi-Hopf Algebras: A Categorical Approach

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.

Daniel Bulacu is Professor in the Faculty of Mathematics and Computer Science at Universitatea din Bucuresti, Romania. His research interests include graded rings and modules, Hopf algebras and generalizations, (braided) monoidal categories, braid groups, Clifford algebras, Cayley-Dickson algebras, (co)Frobenius (co)algebras, (co)wreaths and derived (co)wreath (co)algebra structures, and Hopf Galois theory. He received the 2009 'Dimitrie Pompeiu' prize from the Romanian Academy. Stefaan Caenepeel is Professor in the Faculty of Engineering at the Vrije Universiteit Brussel (VUB). His research interests include graded rings and modules, Hopf algebras and their generalizations, Brauer groups, monoidal categories and categorical algebra. He was president of the Belgian Mathematical Society (2008-2011) and is currently dean of the Faculty of Engineering at VUB (2016-2020). Florin Panaite is Scientific Researcher at the Institute of Mathematics of the Romanian Academy. His research interests include Hopf algebras and generalizations (quasi-Hopf algebras, bialgebroids), (braided) monoidal categories, braid groups, Clifford algebras, Cayley-Dickson algebras, twisted tensor products of algebras, Brzezinski crossed products, twistings of algebras and Rota-Baxter type operators, and Hom-structures. He received the 1999 'Gheorghe Lazar' prize from the Romanian Academy. Freddy Van Oystaeyen is Professor Emeritus at Universiteit Antwerpen, Belgium, Honorary Professor at Beijing Normal University and Doctor Honoris Causa at the Universidad de Almeria, Spain. He has (co)authored more than 300 papers and twenty-five books, and is editor of more than twenty proceedings of international congresses. He has organized more than sixty international meetings and made research evaluations for the Belgian Science Foundation (FWO), as well as in the Netherlands and Romania. He was member of the AAC for the European ERASMUS program.

'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, 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.' Loic Foissy, 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, MathSciNet