Abstract
Abstract
We extend the notion of y-variables (coefficients) in cluster algebras to cluster scattering diagrams (CSDs). Accordingly, we extend the dilogarithm identity associated with a period in a cluster pattern to the one associated with a loop in a CSD. We show that these identities are constructed from and reduced to trivial ones by applying the pentagon identity possibly infinitely many times.
Publisher
Cambridge University Press (CUP)
Reference32 articles.
1. [25] Matsushita, K. , Consistency relations of rank 2 cluster scattering diagrams of affine type and the pentagon relation, preprint, arXiv:2112.04743 [math.QA]
2. Affine structures and non-archimedean analytic spaces;Kontsevich;Prog. Math.,2006
3. Periodicities in cluster algebras and dilogarithm identities
4. Cluster algebras II. Finite type classification;Fomin;Invent. Math.,2003
5. Tropicalization method in cluster algebras;Nakanishi;Contemp. Math.,2012