Hochschild cohomology and derived Picard groups

TL;DR

This paper links Hochschild cohomology to the Lie algebra of the derived Picard group, showing it remains invariant under derived equivalences, thus deepening the understanding of derived categories and their symmetries.

Contribution

It provides a new interpretation of Hochschild cohomology as the Lie algebra of the derived Picard group and proves its invariance under derived equivalences.

Findings

Hochschild cohomology is identified with the Lie algebra of the derived Picard group

Hochschild cohomology is preserved under derived equivalences

The work enhances understanding of symmetries in derived categories

Abstract

We interpret Hochschild cohomology as the Lie algebra of the derived Picard group (in the sense of Rouquier-Zimmermann and Yekutieli) and deduce that it is preserved under derived equivalences.