Finite W-algebras were introduced by Premet in full generality, and they quickly became quite famous for their many applications in the representation theory of complex semisimple Lie algebras, especially the classification of primitive ideals. However, these algebras first appeared in the representation theory of Lie algebras associated to reductive groups in positive characteristic. In this talk I will survey the history of finite W-algebras in modular representation theory, and explain some of the contributions I have made to the field. The main applications in this talk will be the construction and classification of ‘small’ modules of Lie algebras.
This video is part of the European Non-Associative Algebra Seminar series.
