The role of gentle algebras in higher homological algebra
Peer reviewed, Journal article
Accepted version
Åpne
Permanent lenke
https://hdl.handle.net/11250/3052819Utgivelsesdato
2022Metadata
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- Institutt for matematiske fag [2354]
- Publikasjoner fra CRIStin - NTNU [37236]
Sammendrag
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] .