Singularity categories of skewed-gentle algebras

• Autorzy: Xinhong Chen , Ming Lu
• Języki publikacji: EN

Abstrakty

EN

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 $KQ^{sg}/⟨I^{sg}⟩$ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of $KQ^{g}/⟨I^{g}⟩$. As a corollary, we find that $gldim KQ^{sg}/⟨I^{sg}⟩ < ∞$ if and only if $gldim KQ/⟨I⟩ < ∞$ if and only if $gldim KQ^{g}/⟨I^{g}⟩ < ∞$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 141
• Numer: 2
• Strony: 183-198

Daty

wydano

2015

Twórcy

autor

Xinhong Chen

• Department of Mathematics, Southwest Jiaotong University, Chengdu 610031, P.R. China

autor

Ming Lu

• Department of Mathematics, Sichuan University, Chengdu 610064, P.R. China

Identyfikatory

DOI

10.4064/cm141-2-4