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

John W Lawson

Abstract


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.

Keywords


Cluster algebra; Quiver mutation; Cluster automorphism; Exchange graph; Mapping class group

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