A characterisation of τ-tilting finite algebras

Lidia Angeleri Hugel;Frederik Marks;Jorge Nuno Dos Santos Vitoria

2019-01-01

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Abstract

We prove that a finite dimensional algebra is τ-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a τtilting finite algebra A there is a bijection between isomorphism classes of basic support τ-tilting (that is, finite dimensional silting) modules and equivalence classes of ring epimorphisms A → B with TorA1 (B, B) = 0. It follows that a finite dimensional algebra is τ-tilting finite if and only if there are only finitely many equivalence classes of such ring epimorphisms.