February 8, 2010, 2:10 pm

Bahen 6183

Abstract:Varieties of structure constants of complex n-dimensional Lie algebras were studied by Kirillov, Neretin, and others. Let G be a finite abelian group. Following work of Moody and Patera, one can consider algebraic varieties parametrizing G-graded Lie algebra structures on a fixed (G-graded) finite-dimensional complex vector space. I will talk about joint work with M. Tvalavadze where we prove, in particular, that the first homology group of an irreducible component of this variety, under certain assumptions, is trivial.