GLS-代数的奇点范畴

Singularity categories of GLS-algebras

摘要:

设$H$是GLS-代数，$D_{sg}({\rm{mod}}^{\mathbb{Z}} H)$是其有限维$\Z$-分次$H$-模的奇点范畴. 本文证明了$D_{sg}({\rm{mod}}^{\mathbb{Z}} H)$存在倾斜对象，从而$D_{sg}({\rm{mod}}^{\mathbb{Z}} H)$ 三角等价于某个代数投射模的有界同伦范畴.

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 $D_{sg}({\rm{mod}}^{\mathbb{Z}} H)\simeq K^b(\proj(\End(T)^{op}))$.