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A Geometric Realization of the m-cluster Categories of Type D∼n.

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Title: A Geometric Realization of the m-cluster Categories of Type D∼n.
Authors: Jacquet-Malo, Lucie1 (AUTHOR) lucie.jacquet.malo@u-picardie.fr
Source: Frontiers of Mathematics. Nov2025, Vol. 20 Issue 6, p1325-1370. 46p.
Subject Terms: *GEOMETRIC modeling, *POLYGONS, *GEOMETRIC shapes
Abstract: We show that a subcategory of the m-cluster category of type D ∼ n is isomorphic to a category consisting of arcs in an (n − 2)m-gon with two central (m − 1)-gons in its interior. We show that the mutation of colored quivers and m-cluster-tilting objects is compatible with the flip of an (m + 2)-angulation. In the final part of this paper, we detail an example of a quiver of type D ∼ 7 . [ABSTRACT FROM AUTHOR]
Database: Academic Search Index
Description
Abstract:We show that a subcategory of the m-cluster category of type D ∼ n is isomorphic to a category consisting of arcs in an (n − 2)m-gon with two central (m − 1)-gons in its interior. We show that the mutation of colored quivers and m-cluster-tilting objects is compatible with the flip of an (m + 2)-angulation. In the final part of this paper, we detail an example of a quiver of type D ∼ 7 . [ABSTRACT FROM AUTHOR]
ISSN:27318648
DOI:10.1007/s11464-023-0133-7