Semilinear clannish algebras arising from surfaces with orbifold points

Abstract

Semilinear clannish algebras have been recently introduced by the first author and Crawley-Boevey as a generalization of Crawley-Boevey's clannish algebras. In the present paper, we associate semilinear clannish algebras to the (colored) triangulations of a surface with marked points and orbifold points, and exhibit a Morita equivalence between these algebras and the Jacobian algebras constructed a few years ago by Geuenich and the second author.

v2: 6 figures, many tables with explicit computations, several editorial changes; 50 pages. v1: 5 figures, several tables with explicit computations; 45 pages