Killing forms are bilinear forms most well-known in the context of Lie algebras. Their definition has been extended to braided-Killing forms on braided-Lie algebras, and applying this to certain braided-Lie algebras based on finite groups yields an expression in terms of centralizers in the group.
In this talk, based on a collaboration with Kevin Piterman, we discuss some problems concerning the non-degeneracy and irreducibility of these forms on finite groups. We cover classes of involutions in simple groups of Lie type and rank 1 and study the case of unipotent elements in PSL(2,q) and the Suzuki groups.Â