Singularity categories of skewed-gentle algebras

Xinhong Chen; Ming Lu

Xinhong Chen ; Ming Lu

Colloquium Mathematicae, Tome 139 (2015), p. 183-198 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $g l d i m K Q^{s g} / ⟨ I^{s g} ⟩ < \infty$ if and only if $g l d i m K Q / ⟨ I ⟩ < \infty$ if and only if $g l d i m K Q^{g} / ⟨ I^{g} ⟩ < \infty$ .

Publié le : 2015-01-01

Zbl 06487237

EUDML-ID : urn:eudml:doc:283798

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     title = {Singularity categories of skewed-gentle algebras},
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     volume = {139},
     year = {2015},
     pages = {183-198},
     zbl = {06487237},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-4}
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Xinhong Chen; Ming Lu. Singularity categories of skewed-gentle algebras. Colloquium Mathematicae, Tome 139 (2015) pp. 183-198. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm141-2-4/