Projects
Simple linear algebraic groups: representation theory and subgroup structure KU Leuven
This research project concerns the representation theory and the subgroup structure of simple linear algebraic groups. These two topics are very closely related, as for example the study of subgroups of classical groups is essentially the study of representations of groups. Two major open problems for researchers in this field are understanding the irreducible representations of simple linear algebraic groups and classifying their reductive ...
Braided quantum groups, actions and von Neumann algebras Vrije Universiteit Brussel
Quantum groups, Hopf algebras and tensor categories. Hasselt University
Non-associative algebras for exceptional groups Ghent University
Linear algebraic groups are matrix groups defined by polynomials. In the past century, a lot of research has been done to develop a classification of these algebraic groups. Among the objects of most interest in this theory are the exceptional groups. Though their classification is complete, a lot of questions remain about these mysterious objects. Recently, a class of algebras that have these exceptional groups as symmetries have been ...
Locally compact groups and von Neumann algebras KU Leuven
Von Neumann algebra theory is a branch of functional analysis dealing with weakly closed algebras of bounded operators on a Hilbert space and was developed by Murray and von Neumann in the 1940s, in order to put quantum mechanics into a solid mathematical framework. The most fundamental families of von Neumann algebras arise from a crossed product type construction, starting from actions of groups. Thanks to Sorin Popa's deformation/rigidity ...
Distinguishing Groups and Algebras via Growth Functions and Representations Vrije Universiteit Brussel
An invariant is a number or geometric object associated with the algebra or ...