- Journal Article
We show that the repetitive higher cluster category of type An, deﬁned as the orbit category Db(mod kAn)/(τ−1[m])p, is equivalent to a category deﬁned on a subset of diagonals in a regular polygon. This generalizes the construction of Caldero–Chapoton–Schiﬄer [Quivers with relations arising from clusters (Ancase), Trans. Amer. Math.Soc. 358(3) (2006) 1347–1364], which we recover when p = m =1,and the work of Baur–Marsh, [A geometric description of the m-cluster categories, Trans. Amer. Math.Soc. 360(11) (2008) 5789–5803], treating the case p =1,m>1. Our approach also leads to a geometric model of the bounded derived category in type A. Show more
Journal / seriesJournal of Algebra and Its Applications
Pages / Article No.
SubjectRepetitive cluster categories; Cluster categories; Cluster combinatorics; Triangulations of polygons
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