2017/06/07 by Igusa, Kiyoshi, Todorov, Gordana · 3 citations
#16G20 #20F55 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.1706.02041
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→ \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|∈ \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].