Aarhus Universitets segl

The role of gentle algebras in higher homological algebra

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review



  • 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].

TidsskriftForum Mathematicum
Sider (fra-til)1255-1275
Antal sider21
StatusUdgivet - 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.

Se relationer på Aarhus Universitet Citationsformater

ID: 295633872