2023/08/30 by Faber, Eleonore, Marsh, Bethany Rose, Pressland, Matthew · 1 citation
#Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2308.16232
We describe a reduction technique for stably 2-Calabi--Yau Frobenius extriangulated categories F with respect to a functorially finite rigid subcategory X. The reduction of such a category is another category X⊥1\subseteqF of the same kind, whose cluster-tilting subcategories are those cluster-tilting subcategories T\subseteqF such that X\subseteqT. This reduction operation generalises Iyama--Yoshino's reduction for 2-Calabi--Yau triangulated categories, which is recovered by passing to stable categories. Moreover, for a certain class of categories F and rigid objects M, we show that the relationship between F and M⊥1 may also be expressed in terms of internally Calabi--Yau algebras, in the sense of the third author. As an application, we give a conceptual proof of a result on frieze patterns originally obtained by the first author with Baur, Gratz, Serhiyenko, and Todorov.