Cluster automorphisms and the marked exchange graphs of skew-symmetrizable cluster algebras [article]

John W. Lawson
2016 arXiv   pre-print
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 aim to 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.
arXiv:1602.05494v2 fatcat:gtdzq7odo5hbvomkfl7d725frq