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Abstract
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We show that a gentle algebra over a field is
-tilting
finite if and only if it is representation-finite. The proof relies on the
“brick--tilting
correspondence” of Demonet, Iyama, and Jasso and on a combinatorial analysis.
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Keywords
representation theory, $\tau$-tilting theory, finite
representation type, gentle algebras
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Mathematical Subject Classification 2010
Primary: 16G20
Secondary: 16G60
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Milestones
Received: 15 November 2018
Revised: 23 March 2019
Accepted: 23 March 2019
Published: 27 November 2019
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