Graph complexes via Brauer categories and Koszul complexes

Abstract: In this talk I will explain new perspectives on the graph complexes associated to a cyclic operad by using modules over twisted k-linearizations of the appropriate Brauer category. This leads to two interesting Koszul complexes, one corresponding to the (hairy) graph complex. The second complex is a precursor of the Chevalley-Eilenberg complex of the family of Lie algebras associated to a cyclic operad by Kontsevich, as developed by Conant-Vogtmann. The relationship between these complexes reflects the stabilization, as interpreted using methods of Sam and Snowden, governed by the twisted Brauer category. There is an analogous story for operads, related to recent work of Dotsenko starting from derivations of free algebras over the operad; this uses walled Brauer categories.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar