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Semiorthogonal decompositions for bounded derived categories of gentle algebras

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arxiv 2209.14496 v1 pith:GXQTR4IG submitted 2022-09-29 math.RT math.CT

Jakub Kopřiva , Jan Šťovíček This is my paper · ORCID
classification math.RTmath.CT
keywords categoriesdecompositionssemiorthogonalalgebrasboundedderivedgentlegeometric
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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.

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  1. Tilting-completion for gentle algebras

    math.RT 2024-12 conditional novelty 6.0 of 10

    For gentle algebras, almost-tilting modules always complete to tilting modules with at most 2n complements, matching a modified version of Happel's conjecture.

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