Singularity categories of GLS-algebras

Abstract:

Let $H$ be a GLS-algebra and $D_{sg}({\rm{mod}}^{\mathbb{Z}} H)$ be the singularity category of finite-dimensional $\Z$-graded $H$-modules. In this paper we prove that $D_{sg}({\rm{mod}}^{\mathbb{Z}} H)$ admits a tilting object $T$, and therefore $D_{sg}({\rm{mod}}^{\mathbb{Z}} H)\simeq K^b(\proj(\End(T)^{op}))$.