$\tau$-Tilting Finite Algebras With Nonempty Left Or Right Parts Are Representation-Finite

Abstract

Let $\Lambda$ be a finite dimensional algebra such that ${\mathcal{L}}_{\Lambda }$ or ${\mathcal{R}}_{\Lambda }\ne \varnothing$. Then $\Lambda$ is $\tau$-tilting finite if and only if $\Lambda$ is representation-finite.

Main result is incorrect due to a misapplication of Proposition 2.7. Counterexamples have been found