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We investigate the role of gentle algebras in higher homological algebra. In the first part of the paper, we show that if the module category of a gentle algebra Λ contains a d-cluster tilting subcategory for some d ≥ 2, then Λ is a radical square zero Nakayama algebra. This gives a complete classification of weakly d-representation finite gentle algebras. In the second part, we use a geometric model of the derived category to prove a similar result in the triangulated setup. More precisely, we show that if Db(Λ) contains a d-cluster tilting subcategory that is closed under [d], then Λ is derived equivalent to an algebra of Dynkin type A. Furthermore, our approach gives a geometric characterization of all d-cluster tilting subcategories of Db(Λ) that are closed under [d].
Original language | English |
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Journal | Forum Mathematicum |
Volume | 34 |
Issue | 5 |
Pages (from-to) | 1255-1275 |
Number of pages | 21 |
ISSN | 0933-7741 |
DOIs | |
Publication status | Published - Sept 2022 |
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