Lie algebra representations and free Jordan algebras

Abstract: For any unital Jordan algebra, the famous Tits-Kantor-Koecher construction produces an sl(2)-graded Lie algebra. We will look at weight modules for universal central extensions of these algebras, concentrating on categories of modules satisfying combinatorial dominance or smoothness conditions. We describe some finiteness results for algebras and Weyl modules in these contexts. Surprisingly, the proofs of several of our results use Zelmanov's theorem on nil Jordan algebras of bounded index. This talk is based on joint work with Olivier Mathieu.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar