Singularity categories of skewed-gentle algebras
Chen, Xinhong · Lu, Ming
Original · EN
Let K be an algebraically closed field. Let (Q,Sp,I) be a skewed-gentle triple, (Qsg,Isg) and (Qᵍ,Iᵍ) be its corresponding skewed-gentle pair and associated gentle pair respectively. It proves that the skewed-gentle algebra KQsg/< Isg> is singularity equivalent to KQ/< I>. Moreover, we use (Q,Sp,I) to describe the singularity category of KQᵍ/< Iᵍ>. As a corollary, we get that gldim KQsg/< Isg><∞ if and only if gldim KQ/< I><∞ if and only if gldim KQᵍ/< Iᵍ><∞.
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