Academic Journal
Mutation graph of support -tilting modules over a skew-gentle algebra.
| Τίτλος: | Mutation graph of support -tilting modules over a skew-gentle algebra. |
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| Πηγή: | Forum of Mathematics, Sigma. 2025, Vol. 13, p1-43. 43p. |
| Θεματικοί όροι: | *Mutations (Algebra), *Modules (Algebra), *Algebra, *Triangulated categories |
| Περίληψη: | Let $\mathcal {D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object R. Let $\Lambda =\operatorname {End}_{\mathcal {D}}R$ be the endomorphism algebra of R. We introduce the notion of mutation of maximal rigid objects in the two-term subcategory $R\ast R[1]$ via exchange triangles, which is shown to be compatible with the mutation of support $\tau $ -tilting $\Lambda $ -modules. In the case that $\mathcal {D}$ is the cluster category arising from a punctured marked surface, it is shown that the graph of mutations of support $\tau $ -tilting $\Lambda $ -modules is isomorphic to the graph of flips of certain collections of tagged arcs on the surface, which is moreover proved to be connected. Consequently, the mutation graph of support $\tau $ -tilting modules over a skew-gentle algebra is connected. This generalizes one main result in [49]. [ABSTRACT FROM AUTHOR] |
| Βάση Δεδομένων: | Academic Search Index |
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| Items | – Name: Title Label: Title Group: Ti Data: Mutation graph of support -tilting modules over a skew-gentle algebra. – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Forum+of+Mathematics%2C+Sigma%22">Forum of Mathematics, Sigma</searchLink>. 2025, Vol. 13, p1-43. 43p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Mutations+%28Algebra%29%22">Mutations (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Modules+%28Algebra%29%22">Modules (Algebra)</searchLink><br />*<searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br />*<searchLink fieldCode="DE" term="%22Triangulated+categories%22">Triangulated categories</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Let $\mathcal {D}$ be a Hom-finite, Krull-Schmidt, 2-Calabi-Yau triangulated category with a rigid object R. Let $\Lambda =\operatorname {End}_{\mathcal {D}}R$ be the endomorphism algebra of R. We introduce the notion of mutation of maximal rigid objects in the two-term subcategory $R\ast R[1]$ via exchange triangles, which is shown to be compatible with the mutation of support $\tau $ -tilting $\Lambda $ -modules. In the case that $\mathcal {D}$ is the cluster category arising from a punctured marked surface, it is shown that the graph of mutations of support $\tau $ -tilting $\Lambda $ -modules is isomorphic to the graph of flips of certain collections of tagged arcs on the surface, which is moreover proved to be connected. Consequently, the mutation graph of support $\tau $ -tilting modules over a skew-gentle algebra is connected. This generalizes one main result in [49]. [ABSTRACT FROM AUTHOR] |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=191132275 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1017/fms.2025.49 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 43 StartPage: 1 Subjects: – SubjectFull: Mutations (Algebra) Type: general – SubjectFull: Modules (Algebra) Type: general – SubjectFull: Algebra Type: general – SubjectFull: Triangulated categories Type: general Titles: – TitleFull: Mutation graph of support -tilting modules over a skew-gentle algebra. Type: main BibRelationships: IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 20505094 Numbering: – Type: volume Value: 13 Titles: – TitleFull: Forum of Mathematics, Sigma Type: main |
| ResultId | 1 |