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.

15 pages, the proof of Theorem 4.11 revised, reference added

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