Singularity categories of skewed-gentle algebras

Xinhong Chen, and Ming Lu. "Singularity categories of skewed-gentle algebras." Colloquium Mathematicae 141.2 (2015): 183-198. <http://eudml.org/doc/283798>.

@article{XinhongChen2015,
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 $KQ^\{sg\}/⟨I^\{sg\}⟩$ 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 $gldim KQ^\{g\}/⟨I^\{g\}⟩ < ∞$.},
author = {Xinhong Chen, Ming Lu},
journal = {Colloquium Mathematicae},
keywords = {gentle algebras; skewed-gentle algebras; Gorenstein algebras; singularity categories},
language = {eng},
number = {2},
pages = {183-198},
title = {Singularity categories of skewed-gentle algebras},
url = {http://eudml.org/doc/283798},
volume = {141},
year = {2015},
}

TY - JOUR
AU - Xinhong Chen
AU - Ming Lu
TI - Singularity categories of skewed-gentle algebras
JO - Colloquium Mathematicae
PY - 2015
VL - 141
IS - 2
SP - 183
EP - 198
AB - 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 $gldim KQ^{g}/⟨I^{g}⟩ < ∞$.
LA - eng
KW - gentle algebras; skewed-gentle algebras; Gorenstein algebras; singularity categories
UR - http://eudml.org/doc/283798
ER -