$\tau$-Tilting Finite Cluster-Tilted Algebras

Abstract

Let B be a cluster-tilted algebra. We prove that B is $\tau$-tilting finite if and only if B is representation-finite.

arXiv comment9 pages. Removed the proof concerning tilted algebras. The proof is still contained in v1. Corrected the proof concerning cluster-tilted algebras

References in corpus (2)

• $\tau$-tilting finite algebras, bricks and $g$-vectors
• Unramified cohomology of classifying varieties for exceptional simply connected groups

Cited by in corpus (7)

• On $\tau$-tilting finiteness of the Schur algebra
• Report on the finiteness of silting objects
• Schurian-finiteness of blocks of type $A$ Hecke algebras
• $\tau$-tilting finiteness of two-point algebras II
• On $\tau$-tilting finiteness of symmetric algebras of polynomial growth
• Three results for tau-rigid modules
• Self-orthogonal tau-tilting modules and tilting modules