Bases for cluster algebras from orbifolds

Felikson, A.; Tumarkin, P.

Abstract

We generalize the construction of the bracelet and bangle bases defined in [36] and the band basis defined in [43] to cluster algebras arising from orbifolds. We prove that the bracelet bases are positive, and the bracelet basis for the affine cluster algebra of type Cn(1) is atomic. We also show that cluster monomial bases of all skew-symmetrizable cluster algebras of finite type are atomic.

Citation

Felikson, A., & Tumarkin, P. (2017). Bases for cluster algebras from orbifolds. Advances in Mathematics, 318, 191-232. https://doi.org/10.1016/j.aim.2017.07.025

• Journal Article Type: Article
• Acceptance Date: Jul 26, 2017
• Online Publication Date: Aug 2, 2017
• Publication Date: Oct 1, 2017
• Deposit Date: Apr 4, 2016
• Publicly Available Date: Aug 2, 2018
• Journal: Advances in Mathematics
• Print ISSN: 0001-8708
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 318
• Pages: 191-232
• DOI: https://doi.org/10.1016/j.aim.2017.07.025
• Public URL: https://durham-repository.worktribe.com/output/1387898
• Related Public URLs: http://arxiv.org/abs/1511.08023