Generalized weighted surface algebras
Abstract
The weighted triangulation algebras associated to triangulation quivers and their socle deformations were recently introduced and studied in [15]-[20] and [2]. These algebras, based on surface triangulations and originated from the theory of cluster algebras, were also proved to be (with some minor exceptions) finite-dimensional tame symmetric and periodic algebras of period 4. In this paper, we introduce a new concept of a generalized triangulation quiver, extending the notion of a triangulation quiver. Inparticular, it is also shown that the generalized triangulation quivers can be constructed from triangulations of orientable surfaces with marked self-foldedtriangles. Moreover, motivated by the recent results of [28], we define and investigate so called weighted generalized triangulation algebras associated to generalized triangulation quivers, which naturally arise from mutations of weighted triangulation algebras.
Cite
@article{arxiv.2106.15218,
title = {Generalized weighted surface algebras},
author = {Andrzej Skowroński and Adam Skowyrski},
journal= {arXiv preprint arXiv:2106.15218},
year = {2025}
}