The quiver with superpotentials of a $d$-angulation of a marked surface
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909864304836608 |
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| author | Le, Bo Zhu, Bin |
| author_facet | Le, Bo Zhu, Bin |
| contents | In this paper, we associate a quiver with superpotential to each $d$-angulation of a (unpunctured) marked surface. We show that, under quasi-isomorphisms, the flip of a $d$-angulation is compatible with Oppermann's mutation of (the Ginzburg algebra of) the corresponding quiver with superpotential, thereby partially generalizing the result in [LF09]. Applying to the generalized $(d-2)$-cluster categories associated to this quiver with superpotential, we prove that some certain almost complete $(d-2)$-cluster tilting objects in the higher cluster category have exactly $d-1$ complements. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_00435 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The quiver with superpotentials of a $d$-angulation of a marked surface Le, Bo Zhu, Bin Representation Theory Rings and Algebras In this paper, we associate a quiver with superpotential to each $d$-angulation of a (unpunctured) marked surface. We show that, under quasi-isomorphisms, the flip of a $d$-angulation is compatible with Oppermann's mutation of (the Ginzburg algebra of) the corresponding quiver with superpotential, thereby partially generalizing the result in [LF09]. Applying to the generalized $(d-2)$-cluster categories associated to this quiver with superpotential, we prove that some certain almost complete $(d-2)$-cluster tilting objects in the higher cluster category have exactly $d-1$ complements. |
| title | The quiver with superpotentials of a $d$-angulation of a marked surface |
| topic | Representation Theory Rings and Algebras |
| url | https://arxiv.org/abs/2501.00435 |