Singularity categories of skewed-gentle algebras

Abstract

Let $K$ be an algebraically closed field. Let $(Q,Sp,I)$ be a skewed-gentle triple, $(Q^{sg},I^{sg})$ and $(Q^g,I^g)$ be its corresponding skewed-gentle pair and associated gentle pair respectively. It proves that the skewed-gentle algebra $K{Q}^{sg}/<I^{sg}>$ is singularity equivalent to $KQ/<I>$. Moreover, we use $(Q,Sp,I)$ to describe the singularity category of $K{Q}^g/<I^g>$. As a corollary, we get that $\mathrm{gldim}K{Q}^{sg}/<I^{sg}><\infty$ if and only if $\mathrm{gldim}KQ/<I><\infty$ if and only if $\mathrm{gldim}K{Q}^g/<I^g><\infty$.

13 pages, 1 figure

References in corpus (1)

• On triangulated orbit categories