Singularity categories of skewed-gentle algebras
Volume 141 / 2015
Colloquium Mathematicum 141 (2015), 183-198
MSC: 16G20, 16E35, 18E30.
DOI: 10.4064/cm141-2-4
Abstract
Let $K$ be an algebraically closed field. Let $(Q,Sp,I)$ be a skewed-gentle triple, and let $(Q^{sg},I^{sg})$ and $(Q^g,I^{g})$ be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra $KQ^{sg}/\langle I^{sg}\rangle$ is singularity equivalent to $KQ/\langle I\rangle$. Moreover, we use $(Q,Sp,I)$ to describe the singularity category of $KQ^g/\langle I^g\rangle$. As a corollary, we find that $\operatorname{gldim} KQ^{sg}/\langle I^{sg}\rangle<\infty$ if and only if $\operatorname{gldim} KQ/\langle I\rangle<\infty$ if and only if $\operatorname{gldim} KQ^{g}/\langle I^{g}\rangle<\infty$.
