Quasi-Hopf Algebras

Daniel Bulacu is Professor in the Faculty of Mathematics and Computer Science at the Universitatea din Bucureşti, 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 the VUB (2016-2020). Florin Panaite is Scientific Researcher at the Institute of Mathematics of 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 Honorary Professor at Beijing Normal University and Doctor Honoris Causa at University de Almeria. He has (co)authored over 300 papers and twenty-five books, and is the editor of over twenty proceedings of international congresses. He has organized more than sixty international meetings and made research evaluations for the Belgian Science Foundation (FWO), also 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

• 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.