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Signed exceptional sequences and the cluster morphism category

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arxiv 1706.02041 v1 pith:2YUOH2UY submitted 2017-06-07 math.RT

Kiyoshi Igusa , Gordana Todorov This is my paper · ORCID
classification math.RT
keywords categorymathcalmorphismclusterexceptionalsignedalgebrafactorizations
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abstract

We introduce signed exceptional sequences as factorizations of morphisms in the cluster morphism category. The objects of this category are wide subcategories of the module category of a hereditary algebra. A morphism $[T]:\mathcal A\to \mathcal B$ is the equivalence class of a rigid object $T$ in the cluster category of $\mathcal A$ so that $\mathcal B$ is the right hom-ext perpendicular category of the underlying object $|T|\in \mathcal A$. Factorizations of a morphism $[T]$ are given by total orderings of the components of $T$. This is equivalent to a "signed exceptional sequence." For an algebra of finite representation type, the geometric realization of the cluster morphism category is an Eilenberg-MacLane space with fundamental group equal to the "picture group" introduced by the authors in [IOTW4].

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Cited by 3 Pith papers

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  1. A higher homological approach to the $q$-characters of representations of quantum affine algebras

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    Introduces presilting sequences in 0-Auslander extriangulated categories with a bijection to tau-exceptional sequences and defines a new tau-cluster morphism category M(C).

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