Let L be a graded Lie algebra by integers with k-th homogenous space Lk where k are integers. An L-module V is called a smooth module if any vector in V can be annihilated by Lk for all sufficiently large k. Smooth modules for affine Kac-Moody algebras were introduced and studied by Kazhdan and Lusztig in 1993. I will show why this class of modules should be studied and what results are known now. An easy characterization for simple smooth modules for some Lie algebras will be provided.
This video is part of the European Non-Associative Algebra Seminar series.
