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A note on cluster automorphism groups

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arxiv 1812.05034 v2 pith:SXD2RUY3 submitted 2018-12-12 math.RT math.RA

Wen Chang , Ralf Schiffler This is my paper · ORCID
classification math.RTmath.RA
keywords clusteralgebraautomorphismclustersconjectureautomorphismsbijectionbipartite
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We conjecture a characterization of a cluster automorphism as an algebra homomorphism from the cluster algebra to itself that restricts to a bijection between two clusters. This formulation does not require that the map commutes with mutations as in the original definition of cluster automorphisms. We prove the conjecture in the case where at least one of the two clusters is bipartite.

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  1. A conjecture on cluster automorphisms of cluster algebras

    math.RT 2019-08 conditional novelty 7.0 of 10

    The paper proves that any Z-algebra homomorphism of a cluster algebra mapping one cluster to another is a cluster automorphism, confirming Chang-Schiffler's conjecture.

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