Singularity categories of skewed-gentle algebras
X Chen, M Lu - arXiv preprint arXiv:1409.5960, 2014 - arxiv.org
X Chen, M Lu
arXiv preprint arXiv:1409.5960, 2014•arxiv.orgLet $ 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 $ 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 get that $\mathrm {gldim}
KQ^{sg}/< I^{sg}><\infty $ if and only if $\mathrm {gldim} KQ/< I><\infty $ if and only if …
$(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 $ 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 get that $\mathrm {gldim}
KQ^{sg}/< I^{sg}><\infty $ if and only if $\mathrm {gldim} KQ/< I><\infty $ if and only if …
Let be an algebraically closed field. Let be a skewed-gentle triple, and be its corresponding skewed-gentle pair and associated gentle pair respectively. It proves that the skewed-gentle algebra is singularity equivalent to . Moreover, we use to describe the singularity category of . As a corollary, we get that if and only if if and only if .
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