Tuesday, October 23, 14:00, 7.527
Joseph Loubert, Affine cellularity of KLR algebras.
Affine cellular algebras are a nice class of (usually
infinite-dimensional) algebras having strong representation-theoretic
properties. Given a Lie type \Gamma, there is defined a
Khovanov-Lauda-Rouquier algebra whose representations categorify half
of the corresponding quantum group. It is suspected that all KLR
algebras are affine cellular, and that if \Gamma is of finite type,
then the KLR algebra satisfies an additional property which one might
call affine quasi-heredity. In this talk I will discuss these objects
and explain the current state of knowledge regarding this problem.