Cluster characters for cluster categories with infinite-dimensional morphism spaces

By Pierre-Guy Plamondon. 2010

115 citations recorded by the source corpus.

We prove the existence of cluster characters for Hom-infinite cluster categories. For this purpose, we introduce a suitable mutation-invariant subcategory of the cluster category. We sketch how to apply our results in order to categorify any skew-symmetric cluster algebra. More applications and a comparison to Derksen-Weyman-Zelevinsky's results will be given in a future paper.

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

View Paper: https://www.semanticscholar.org/paper/45b1b08f9473b1eb7dc778d901de5ffc4eeb0eaa

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Citations in the corpus

Quivers with potentials associated to triangulated surfaces, Part III: tagged triangulations and cluster monomials (2011, unknown): “This appropriate interpretation is based in Plamondon’s study [26] [27] [28] of generalized cluster categories whose Hom-spaces are not necessarily finite-dimensional.”
Almost complete cluster tilting objects in generalized higher cluster categories (2010, methodology): “which was presented in [2] for the Hom-finite 2-Calabi-Yau case, and also was presented in [28] for the Jacobi-infinite 2-Calabi-Yau case.”
Maximal rigid subcategories in 2-Calabi-Yau triangulated categories (2010, unknown): “It was proved in [Pla] that for a simple mutation of maximal rigid subcategories R,R′, R ∗ R[1] = R′ ∗ R′[1].”
Derived equivalences from mutations of quivers with potential (2009, background): “Let us point out that mutation of quivers with potential goes back to the insight of mathematical physicists, cf. for example Section 5.2 of [14], Section 2.3 of [6], Section 6 of [15] and Section 3 of [35].”