On Jacobian algebras from closed surfaces

TL;DR

This paper investigates the properties of Jacobian algebras derived from ideal triangulations of closed surfaces, revealing their finite-dimensionality, symmetry, and non-rigidity of associated quivers with potentials.

Contribution

It demonstrates that these Jacobian algebras are finite-dimensional and symmetric, and that the related quivers with potentials are not rigid, providing new insights into their algebraic structure.

Findings

Jacobian algebras are finite-dimensional

Jacobian algebras are symmetric

Quivers with potentials are not rigid

Abstract

We show that the quivers with potentials associated to ideal triangulations of marked surfaces with empty boundary are not rigid, and their completed Jacobian algebras are finite-dimensional and symmetric.