Brick-finite skew-gentle algebras are representation-finite

TL;DR

This paper proves that for skew-gentle algebras, being brick-finite is equivalent to being representation-finite, extending a known result from gentle algebras to a broader class.

Contribution

It generalizes Plamondon's theorem from gentle algebras to skew-gentle algebras, establishing an equivalence between brick-finiteness and representation-finiteness.

Findings

Brick-finite skew-gentle algebras are exactly the representation-finite ones.

The result extends the classification of gentle algebras to skew-gentle algebras.

Provides a characterization linking algebraic finiteness conditions.

Abstract

We show that a skew-gentle algebra is brick-finite if and only if it is representation-finite, generalizing Plamondon's original result for gentle algebras.