Università degli Studi di Padova

“Semilinear clannish algebras arising from surfaces with orbifold points”

Giovedì 11 Luglio 2024, ore 9:30 - Aula 2BC30 - Daniel Labardini Fragoso (Instituto de Matemáticas - UNAM)


Clannish algebras, defined by Crawley-Boevey over thirty years ago, form a class of tame algebras whose indecomposable finite-dimensional modules enjoy explicit parameterizations in terms of strings and bands.

Recently, Bennett-Tennenhaus–Crawley-Boevey have introduced the class of semilinear clannish algebras, where the action of the arrows of the quiver on representations allow the scalars to “come out” up to the application of a field automorphism. On the other hand, Geuenich and myself associated Jacobian algebras to triangulations of surfaces with orbifold points a few years ago, and showed that these algebras behave well under flips and mutations of species with potential.

The aim of the talk is to present joint work with Bennett-Tennenhaus, in which we show that the Jacobian algebras that Geuenich and I constructed are Morita equivalent to semilinear clannish algebras.