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The role of gentle algebras in higher homological algebra
Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avis › Tidsskriftartikel › Forskning › peer review
Links
- https://arxiv.org/pdf/2107.01045.pdf
Accepteret manuskript
DOI
- https://doi.org/10.1515/forum-2021-0311
Forlagets udgivne version
- Johanne Haugland, Norwegian University of Science and Technology ,
- Karin M. Jacobsen
- Sibylle Schroll, University of Cologne
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].
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Forum Mathematicum |
| Vol/bind | 34 |
| Nummer | 5 |
| Sider (fra-til) | 1255-1275 |
| Antal sider | 21 |
| ISSN | 0933-7741 |
| DOI | |
| Status | Udgivet - sep. 2022 |
Bibliografisk note
Funding Information:
This work has been partially supported by project IDUN, funded through the Norwegian Research Council (295920). The second author was partially funded by the Norwegian Research Council via the project “Higher homological algebra and tilting theory” (301046). The third author would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the program Cluster Algebras and Representation Theory, where work on this paper was undertaken. This work was supported by EPSRC grant no. EP/R014604/1.
Publisher Copyright:
© 2022 De Gruyter. All rights reserved.
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