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The Derived Category of Surface Algebras: the Case of the Torus with One Boundary Component

Abstract

In this paper we refine the main result of a previous paper of the author with Grimeland on derived invariants of surface algebras. We restrict to the case where the surface is a torus with one boundary component and give an easily computable derived invariant for such surface algebras. This result permits to give answers to open questions on gentle algebras: it provides examples of gentle algebras with the same AG-invariant (in the sense of Avella-Alaminos and Geiss) that are not derived equivalent and gives a partial positive answer to a conjecture due to Bobiński and Malicki on gentle 2-cycle algebras.

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Correspondence to Claire Amiot.

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Presented by Peter Littelmann.

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Amiot, C. The Derived Category of Surface Algebras: the Case of the Torus with One Boundary Component. Algebr Represent Theor 19, 1059–1080 (2016). https://doi.org/10.1007/s10468-016-9611-x

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  • DOI: https://doi.org/10.1007/s10468-016-9611-x

Keywords

  • Quiver representation
  • Derived categories
  • Triangulations of surfaces
  • Cluster combinatorics
  • Quiver mutation

Mathematics Subject Classification (2010)

  • 16E35
  • 16G20
  • 14F35