Quasi-Hopf Algebras

This comprehensive guide explores Drinfeld's quasi-Hopf algebras, catering to both newcomers and advanced researchers in mathematics and mathematical physics.

This self-contained work is the first to focus entirely on Drinfeld's quasi-Hopf algebras, covering everything from foundational concepts to advanced topics. It offers a thorough introduction to (braided) monoidal categories, which serve as the primary framework for analyzing quasi-Hopf algebras. The book is particularly suitable for graduate students and researchers in the fields of mathematics and mathematical physics, providing a comprehensive guide to the subject.

Quasi-Hopf Algebras is designed to be accessible, with complete proofs for the fundamental ideas and nearly complete proofs for more sophisticated topics. Many of the proofs rely on general categorical results, which can be applied to other types of Hopf algebras, such as Turaev or Zunino Hopf algebras, as well as Hom-Hopf and Hopfish algebras. This makes the book a valuable resource not just for those focused on quasi-Hopf algebras, but for anyone interested in the broader category of monoidal representation algebras.

Newcomers will find a detailed explanation of the necessary tools, including (co)algebras and (braided) monoidal categories, while more experienced readers will appreciate the compilation of recent research findings and open questions that could inspire their own investigations. Overall, Quasi-Hopf Algebras serves as both a foundational text and a comprehensive reference for ongoing research in the area.