MATHEMATICS COLLOQUIUM - Yuri Berest (Cornell University)

Yuri Berest (Cornell University)
Representation Homology

Abstract:  The set of all representations of a Lie algebra a in a finite-dimensional Lie algebra g has a natural structure of an affine scheme, called the representation scheme Repg(a).  The representation functor Repg is not “exact" and can be derived in the sense of non-abelian homological algebra.  In this talk, I will explain the construction and properties of derived representation schemes of Lie algebras and their homology (which we call representation homology).   As a main example, we will consider the derived schemes associated with classical commuting schemes of complex reductive Lie algebras.  We will present a general conjecture about the structure of these derived schemes and discuss its implications. Time permitting, we will also discuss a topological version of representation homology and its relation to higher order Hochschild homology and rational homotopy theory.

Event Date: 
March 31, 2016 - 3:30pm to 4:30pm
213 MLH
Ben Cooper
Calendar Category: