Commutative Algebra Seminar

Title

The A-infinity structure on the Ext algebra of a commutative ring

Abstract

Let R be a Noetherian k-algebra, and for simplicity assume that R is augmented of finite type over k of characteristic zero. The minimal semifree model of R is given by the Chevalley-Eilenberg construction of a Lie(-infinity) coalgebra whose dual is the homotopy Lie algebra $\pi$ of R. Taking the universal enveloping algebra of the latter gives rise to the Ext algebra of k.

In this talk we will show how to calculate the higher products on Ext out of the differential on the minimal semifree model of R. This comes as a byproduct of a formula for A-infinity PBW multiplication on the universal envelope of a Lie-infinity algebra. This is especially tractable when R is a complete intersection, since then the homotopy Lie algebra is so short. This is joint work with Ben Briggs.