2019
DOI: 10.2140/pjm.2019.302.709
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τ-tilting finite gentle algebras are representation-finite

Abstract: We show that a gentle algebra over a field is τ -tilting finite if and only if it is representation-finite. The proof relies on the "brick-τ -tilting correspondence" of Demonet-Iyama-Jasso and on a combinatorial analysis.

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Cited by 21 publications
(12 citation statements)
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“…Gentle algebras are a subclass of special biserial algebras. For these algebras a similar criterion to the one obtained in this paper was given in [24].…”
Section: Theorem 14 (Theorem 41) Let K Be An Algebraically Closed Field and Let A Be A Finite Dimensional K -Algebra Containing A Band Momentioning
confidence: 72%
“…Gentle algebras are a subclass of special biserial algebras. For these algebras a similar criterion to the one obtained in this paper was given in [24].…”
Section: Theorem 14 (Theorem 41) Let K Be An Algebraically Closed Field and Let A Be A Finite Dimensional K -Algebra Containing A Band Momentioning
confidence: 72%
“…In [, Theorem 6.12], it is proven that all derived‐discrete algebras of finite global dimension are silting‐discrete. (5)Every preprojective algebra of Dynkin type is silting‐discrete . (6)Algebras of dihedral, semidihedral or quaternion type are shown to be silting‐discrete in . These are the algebras occurring in Erdmann's classification of tame blocks of group algebras of finite groups. (7)The Brauer graph algebras that are tilting‐discrete are determined in . (8)Gentle algebras are τ‐tilting finite if and only if they are representation‐finite .…”
Section: Classification Resultsmentioning
confidence: 99%
“…For more examples, it was proved that τ -tilting-finite cycle-finite algebras are representation-finite [24]. Recently, the gentle case was verified; τ -tiltingfinite gentle algebras are representation-finite [28]. Now, we give new classes of algebras which satisfy this property.…”
Section: Introductionmentioning
confidence: 90%