Recollements and Hochschild theory

TL;DR

This paper explores how recollements of derived categories of algebras influence tensor product and opposite algebras, linking these structures to smoothness and Hochschild cohomology.

Contribution

It demonstrates that recollements induce similar structures on tensor product and opposite algebras, clarifying their relation to Hochschild cohomology and smoothness.

Findings

Recollements induce recollements of tensor product and opposite algebras.

Connections established between recollements, smoothness, and Hochschild cohomology.

Provides a framework for understanding derived category structures in algebra.

Abstract

It is shown that a recollement of derived categories of algebras induces those of tensor product algebras and opposite algebras respectively, which is applied to clarify the relations between recollements of derived categories of algebras and smoothness and Hochschild cohomology of algebras.