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Pré-Publication, Document De Travail Année : 2022

INDECOMPOSABLE OBJECTS IN THE DERIVED CATEGORY OF A SKEW-GENTLE ALGEBRA USING ORBIFOLDS

Résumé

Skew-gentle algebras are skew-group algebras of certain gentle algebras endowed with a Z 2-action. Using the topological description of Opper, Plamondon and Schroll in [OPS] for the indecomposable objects of the derived category of any gentle algebra, one obtains here a complete description of indecomposable objects in the derived category of any skew-gentle algebras in terms of curves on an orbifold surface.The results presented here are complementary to the ones in [LSV]. First, we obtain a complete classification of indecomposable objects and not of "homotopy strings" and "homotopy bands" which are not always indecomposable. Second, the classification obtained here does not use the combinatorial description of [BMM03], but topological arguments coming from the double cover of the orbifold surface constructed in [AB].
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Dates et versions

hal-03279665 , version 1 (06-07-2021)
hal-03279665 , version 2 (14-01-2022)

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Claire Amiot. INDECOMPOSABLE OBJECTS IN THE DERIVED CATEGORY OF A SKEW-GENTLE ALGEBRA USING ORBIFOLDS. 2022. ⟨hal-03279665v2⟩
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