On indecomposable exceptional modules over gentle algebras

TL;DR

This paper characterizes indecomposable exceptional modules over gentle algebras and shows that certain modules related to non-self-intersecting curves are uniquely determined by their dimension vectors.

Contribution

It provides a new characterization of indecomposable exceptional modules over gentle algebras and links modules from surface geometry to algebraic properties.

Findings

Indecomposable exceptional modules are characterized over gentle algebras.

Modules related to non-self-intersecting curves are uniquely determined by their dimension vectors.

Application to gentle algebras from unpunctured surfaces.

Abstract

We give a characterization of indecomposable exceptional modules over finite dimensional gentle algebras. As an application, we study gentle algebras arising from an unpunctured surface and show that a class of indecomposable modules related to curves without selfintersections, as exceptional modules, are uniquely determined by their dimension vectors.