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Singularity categories of skewed-gentle algebras

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Chen X., Lu M.

Colloquium Mathematicum

2015

tom 141

nr 2

183-198

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 $gldim KQ^{g}/⟨I^{g}⟩ < ∞$.

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1 Colloquium Mathematicum

1 Chen X.

1 Lu M.

1 2015

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Singularity categories of skewed-gentle algebras