Eloísa Grifo

ABSTRACT

The homotopy Lie algebra of a noetherian local ring $R$ encodes homological information about $R$: for example, it detects whether $R$ is a complete intersection. In fact, each nontrivial factorization $R = S/(f)$ for $f$ a regular element in $S$ gives rise to a central element element of degree 2 in the homotopy Lie algebra of $R$. A question of Avramov from 1989 asks whether every such central element arises in this manner. In this talk, we will briefly introduce the homotopy Lie algebra and discuss some of its applications, and answer Avramov’s question (spoiler alert: the answer is no).

This is joint work with Ben Briggs, Josh Pollitz, and Mark Walker.