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The role of gentle algebras in higher homological algebra

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  • 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].

Original languageEnglish
JournalForum Mathematicum
Pages (from-to)1255-1275
Number of pages21
Publication statusPublished - Sept 2022

Bibliographical note

Publisher Copyright:
© 2022 De Gruyter. All rights reserved.

    Research areas

  • (d + 2)-angulated category, d-abelian category, d-cluster tilting subcategory, Gentle algebra, higher homological algebra

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