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- W2783702310 abstract "We prove that a finite dimensional algebra is $tau$-tilting finite if and only if it does not admit large silting modules. Moreover, we show that for a $tau$-tilting finite algebra $A$ there is a bijection between isomorphism classes of basic support $tau$-tilting (that is, finite dimensional silting) modules and equivalence classes of ring epimorphisms $Alongrightarrow B$ with ${rm Tor}_1^A(B,B)=0$. It follows that a finite dimensional algebra is $tau$-tilting finite if and only if there are only finitely many equivalence classes of such ring epimorphisms." @default.
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- W2783702310 date "2018-01-12" @default.
- W2783702310 modified "2023-09-27" @default.
- W2783702310 title "A characterisation of $tau$-tilting finite algebras" @default.
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