A characterisation of 𝜏-tilting finite algebras
Lidia Angeleri Hügel, Frederik Marks, Jorge Vitória · Contemporary mathematics - American Mathematical Society · 2019
We prove that a finite dimensional algebra is τ \tau -tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a τ \tau -tilting finite algebra A A there is a bijection between isomorphism classes of basic support τ \tau -tilting (that is, finite dimensional silting) modules and equivalence classes of ring epimorphisms A ⟶ B A\longrightarrow B with T o r 1 A ( B , B ) = 0 \mathrm {Tor}_1^A(B,B)=0 . It follows that a finite dimensional algebra is τ \tau -tilting finite if and only if there are only finitely many equivalence classes of such ring epimorphisms.