SIGNED EXCEPTIONAL SEQUENCES AND THE CLUSTER MORPHISM CATEGORY

By Kiyoshi Igusa, G. Todorov. 2017

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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 ) : A ! B is an equivalence class of rigid objects T in the cluster category of A so that B is the right hom-ext perpendicular category of the underlying object jTj 2 A. Factorizations of a morphism (T ) are given by totally orderings of the components of T. This is equivalent to a \signed exceptional sequences." For an algebra of nite representation type, the geometric realization of the cluster morphism category is the Eilenberg-MacLane space with fundamental group equal to the \picture group" introduced by the authors in (IOTW15b).

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b408190b4d68a39f8970d98ab073ebb09f7d0521