English

Semiorthogonal decompositions for bounded derived categories of gentle algebras

Representation Theory 2022-09-30 v1 Category Theory

Abstract

We study semiorthogonal decompositions of bounded derived categories of gentle algebras and how they are manifested in the geometric model of these categories as constructed by Opper, Plamondon and Schroll. We prove that there is a one-to-one correspondence between such semiorthogonal decompositions and suitable cuts of the marked surface underlying the geometric model. Our main tool is the characterization of basis morphisms between indecomposable objects due to Arnesen, Laking and Pauksztello.

Keywords

Cite

@article{arxiv.2209.14496,
  title  = {Semiorthogonal decompositions for bounded derived categories of gentle algebras},
  author = {Jakub Kopřiva and Jan Šťovíček},
  journal= {arXiv preprint arXiv:2209.14496},
  year   = {2022}
}

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41 pages