Gentle algebras arising from surfaces with orbifold points

Daniel Labardini-Fragoso (UNAM Mexico City, Mexico)

17-Mar-2022, 12:00-13:00 (2 years ago)

Abstract: Some years ago, Diego Velasco and I associated a gentle algebra to each triangulation of a polygon with one orbifold point of order three, and showed that the \tau-tilting combinatorics of this gentle algebra coincides with the combinatorics of flips of triangulations. Moreover, we showed that whenever one mutates support \tau-tilting pairs, the corresponding Caldero-Chapoton functions obey a generalized cluster exchange formula, which means that the Caldero-Chapoton algebra is isomorphic to a generalized cluster algebra of Chekhov-Shapiro. Generalizing the aforementioned work, in ongoing collaboration Lang Mou and I associate a gentle algebra to each triangulation of any unpunctured surface with orbifold points of order three. We are able to define generalized reflection functors and DWZ-like mutations of representations. This is somewhat surprising, since the quivers we consider are allowed to have loops, and the matrix-mutation classes of their skew-symmetrizable matrices may fail to have acyclic representatives.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

Comments: Meeting Link icms-org-uk.zoom.us/j/82901356928?pwd=NmNReXc5U1M0MUFScEVLMEtyaU56dz09 Meeting ID: 829 0135 6928 Passcode: LAGOON22


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