Witt Lie algebra and the associated primitive ideals

Abstract: In my talk I would like to discuss my joint articles with S. Sierra about the primitive ideals of universal enveloping U(W) and the symmetric algebra S(W) of Witt Lie algebra W and similar Lie algebras (including Virasoro Lie algebra). The key theorem in this setting is that every nontrivial quotient by a two-sided ideal of U(W) or S(W) has finite Gelfand-Kirillov dimension. Together with S. Sierra we enhanced this statement to the description of primitive Poisson ideals of S(W) in terms of certain points on the complex plane plus a few parameters attached to these points. In the end I will try to explain how all these concepts works for the ideals whose quotient has Gelfand-Kirillov dimension 2.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar