$\tau$-tilting finite triangular matrix algebras

Abstract

First, we give a new example of silting-discrete algebras. Second, one explores when the algebra of triangular matrices over a finite dimensional algebra is $\tau$-tilting finite. In particular, we classify algebras over which triangular matrix algebras are $\tau$-tilting finite. Finally, we investigate when a triangular matrix algebra is silting-discrete.

11 pages, major changes: Theorem 3.1(1) and the proof of Theorem 2.1, a new important example: Example 3.4