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A geometric realization of tame categories

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arxiv 1502.06489 v1 pith:B3ONCSBV submitted 2015-02-23 math.RT

Karin Baur , Hermund André Torkildsen This is my paper · ORCID
classification math.RT
keywords arcscategoriesgeometricmodulecategorydescriptionquiverrealization
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abstract

We give a geometric realization of module categories of type $\tilde{A}_n$. We work with oriented arcs to define a translation quiver isomorphic to the Auslander-Reiten quiver of the module category of type $\tilde{A}_n$. To get a description of the module category, we introduce long moves between arcs. These allow us to include the infinite radical in the geometric description. Finally, our results can also be used to describe the corresponding cluster categories by taking unoriented arcs instead.

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  1. A geometric model for the non-$\tau$-rigid modules of type $\widetilde{D}_n$

    math.RT 2025-07 conditional novelty 6.0 of 10

    Colored admissible tagged edges in a twice-punctured disk model the non-tau-rigid modules of type \widetilde{D}_n and satisfy an intersection-dimension formula.

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