On the Hochschild homology of singularity categories

Abstract

Let $k$ be an algebraically closed field and $A$ a finite-dimensional $k$-algebra. In this note, we determine complexes which compute the Hochschild homology of the canonical dg enhancement of the bounded derived category of $A$ and of the canonical dg enhancement of the singularity category of $A$. As an application, we obtain a new approach to the computation of Hochschild homology of Leavitt path algebras.