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    Singularity categories of skewed-gentle algebras

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    Let KK be an algebraically closed field. Let (Q,Sp,I)(Q,Sp,I) be a skewed-gentle triple, (Qsg,Isg)(Q^{sg},I^{sg}) and (Qg,Ig)(Q^g,I^{g}) be its corresponding skewed-gentle pair and associated gentle pair respectively. It proves that the skewed-gentle algebra KQsg/KQ^{sg}/ is singularity equivalent to KQ/KQ/. Moreover, we use (Q,Sp,I)(Q,Sp,I) to describe the singularity category of KQg/KQ^g/. As a corollary, we get that gldimKQsg/<∞\mathrm{gldim} KQ^{sg}/<\infty if and only if gldimKQ/<∞\mathrm{gldim} KQ/<\infty if and only if gldimKQg/<Ig><∞\mathrm{gldim} KQ^{g}/< I^{g}><\infty.Comment: 13 pages, 1 figur
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