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Singularity categories of skewed-gentle algebras

Xinhong Chen;  Ming Lu — 2015

Colloquium Mathematicae

Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, and let ( Q s g , I s g ) and ( Q g , I g ) be the corresponding skewed-gentle pair and the associated gentle pair, respectively. We prove that the skewed-gentle algebra K Q s g / ⟨ I s g ⟩ is singularity equivalent to KQ/⟨I⟩. Moreover, we use (Q,Sp,I) to describe the singularity category of K Q g / ⟨ I g ⟩ . As a corollary, we find that g l d i m K Q s g / ⟨ I s g ⟩ < ∞ if and only if g l d i m K Q / ⟨ I ⟩ < ∞ if and only if g l d i m K Q g / ⟨ I g ⟩ < ∞ .

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