A remark on Hochschild cohomology and Koszul duality

TL;DR

This paper demonstrates that Hochschild cohomology, structured as a Gerstenhaber algebra, remains invariant under Koszul-Moore duality by establishing a quasi-isomorphism between their Hochschild complexes.

Contribution

It shows Hochschild cohomology is preserved under Koszul-Moore duality as a Gerstenhaber algebra via B-infinity-algebra quasi-isomorphisms.

Findings

Hochschild cohomology is preserved under Koszul-Moore duality.

Hochschild complexes are linked by a quasi-isomorphism of B-infinity-algebras.

Hochschild cohomology retains its Gerstenhaber algebra structure.

Abstract

Applying recent results by Lowen-Van den Bergh we show that Hochschild cohomology is preserved under Koszul-Moore duality as a Gerstenhaber algebra. More precisely, the corresponding Hochschild complexes are linked by a quasi-isomorphism of B-infinity-algebras.