Action of the Grothendieck-Teichmueller group on the operad of Gerstenhaber algebras

TL;DR

This paper defines an action of the graded Grothendieck-Teichmueller group on a Gerstenhaber algebra operad resolution and proves that this action induces a non-trivial homotopical Lie algebra action.

Contribution

It introduces a new action of the graded GT group on Gerstenhaber operads and demonstrates its homotopical non-triviality, revealing deep algebraic symmetries.

Findings

The GT group acts on a Gerstenhaber operad resolution.

The induced Lie algebra action is homotopically non-trivial.

The map from the GT Lie algebra to the deformation complex is injective.

Abstract

Action of the graded Grothendieck-Teichmueller (GT) group on a resolution of the operad of Gerstenhaber algebras (GA) is defined. It is shown that the induced Lie algebra action is homotopically non-trivial (i.e. the induced map from the Lie algebra of the graded GT group to the deformation complex of the operad of GA is injective).