As a classical group describes the symmetries of the space upon which it acts, a Hopf algebra can be understood as the algebraic object that describes the symme- tries of a non-commutative space which is encoded by an algebra upon which this Hopf algebra (co)acts. Over the last few decades, many variations on the notion of a Hopf algebra have been introduced, inspired by various branches of mathematics.

Among the most promising ideas are multiplier Hopf algebras, Hopfish algebras and Hopf monads. Each one of these variations allows to describe better the symmetries of another type of non-commutative spaces. In this project researchers will investigate the interrelation between these theories. By combining aspects of the different theories, they will be able to describe a larger class of non-commutative spaces and their sym- metries, coming closer to the ultimate goal of a unified theory.


Joost Vercruysse

Mathematics Department, Discrete Mathematics Service
Faculty of Sciences

Created on August 31, 2018