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.
This self-contained book dedicated to Drinfeld's quasi-Hopf algebras takes the reader from the basics to the state of the art.
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
'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