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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