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.
A characterisation of τ-tilting finite algebras
Jorge Nuno Dos Santos Vitoria
2019-01-01
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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
A-characterisation-of-tau-tilting-finite-algebras-revised.pdf
Solo gestori archivio
Tipologia:
versione post-print (AAM)
Dimensione
365.05 kB
Formato
Adobe PDF
|
365.05 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.