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Cluster automorphisms and the marked exchange graphs of skew-symmetrizable cluster algebras
John W Lawson1
1Durham University
The electronic journal of combinatorics, Tome 23 (2016) no. 4
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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.
DOI : 10.37236/6230
Classification : 13F60, 20F34
Mots-clés : cluster algebra, quiver mutation, cluster automorphism, exchange graph, mapping class group

John W Lawson  1

1 Durham University 
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John W Lawson. Cluster automorphisms and the marked exchange graphs of skew-symmetrizable cluster algebras. The electronic journal of combinatorics, Tome 23 (2016) no. 4. doi: 10.37236/6230

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