Report on the finiteness of silting objects

Abstract

We discuss the finiteness of (two-term) silting objects. First, we investigate new triangulated categories without silting object. Second, one studies two classes of $\tau$-tilting-finite algebras and give the numbers of their two-term silting objects. Finally, we explore when $\tau$-tilting-finiteness implies representatoin-finiteness, and obtain several classes of algebras in which a $\tau$-tilting-finite algebra is representation-finite.

arXiv comment15 pages, the proof of Theorem 4.11 revised, reference added

References in corpus (6)

• Silting mutation in triangulated categories
• A reduction theorem for $\tau$-rigid modules
• Classification of two-term tilting complexes over Brauer graph algebras
• Classifying tilting complexes over preprojective algebras of Dynkin type
• $\tau$-Tilting Finite Cluster-Tilted Algebras
• $\tau$-tilting finite gentle algebras are representation-finite

Cited by in corpus (3)

• On $\tau$-tilting finiteness of the Schur algebra
• Schurian-finiteness of blocks of type $A$ Hecke algebras
• On $\tau$-tilting finiteness of symmetric algebras of polynomial growth