Cluster Automorphisms and the Marked Exchange Graphs of Skew-Symmetrizable Cluster Algebras

  • John W Lawson
Keywords: Cluster algebra, Quiver mutation, Cluster automorphism, Exchange graph, Mapping class group


Cluster automorphisms have been shown to have links to the mapping class groups of surfaces, maximal green sequences and to exchange graph automorphisms for skew-symmetric cluster algebras. In this paper we generalise these results to the skew-symmetrizable case by introducing a marking on the exchange graph. Many skew-symmetrizable matrices unfold to skew-symmetric matrices and we consider how cluster automorphisms behave under this unfolding with applications to coverings of orbifolds by surfaces.
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