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

Lawson, J.W.

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.

Citation

Lawson, J. (2016). Cluster automorphisms and the marked exchange graphs of skew-symmetrizable cluster algebras. Electronic Journal of Combinatorics, 23(4), Article P4.41

• Journal Article Type: Article
• Acceptance Date: Nov 30, 2016
• Online Publication Date: Dec 9, 2016
• Publication Date: Jan 1, 2016
• Deposit Date: Sep 7, 2016
• Publicly Available Date: Dec 9, 2016
• Journal: Electronic Journal of Combinatorics
• Electronic ISSN: 1077-8926
• Publisher: Electronic Journal of Combinatorics
• Peer Reviewed: Peer Reviewed
• Volume: 23
• Issue: 4
• Article Number: P4.41
• Public URL: https://durham-repository.worktribe.com/output/1405350
• Publisher URL: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v23i4p41
• Related Public URLs: http://arxiv.org/abs/1602.05494