Commutative Algebra Seminar

Title

Varieties for elementary subalgebras of modular Lie algebras

Abstract

Motivated by questions in modular representation theory, Carlson, Friedlander and the speaker instigated the study of projective varieties of abelian p-nilpotent subalgebras of a fixed dimension r for a p-Lie algebra g. These varieties are closely related to the much studied class of varieties of r-tuples of commuting p-nilpotent matrices which remain highly mysterious when r>2.

In this talk, I shall present some of the representation-theoretic motivation behind the study of these varieties and describe their geometry in a very special case when it is well understood: namely, when r is the maximal dimension of an abelian p-nilpotent subalgebra of a semisimple Lie algebra g.

This is joint work with J. Stark.