Dilogarithm identities in cluster scattering diagrams
Combinatorics
2024-07-09 v4 Quantum Algebra
Abstract
We extend the notion of -variables (coefficients) in cluster algebras to cluster scattering diagrams. Accordingly, we extend the dilogarithm identity associated with a period in a cluster pattern to the one associated with a loop in a cluster scattering diagram. We show that these identities are constructed from and reduced to a trivial one by applying the pentagon identity possibly infinitely many times.
Keywords
Cite
@article{arxiv.2111.09555,
title = {Dilogarithm identities in cluster scattering diagrams},
author = {Tomoki Nakanishi},
journal= {arXiv preprint arXiv:2111.09555},
year = {2024}
}
Comments
v1: 20 pp; v2: 20pp, minor changes in Sec 2.1; v3: 22pp, Thm. 3.4, modified and proof revised; Thm. 4.6 (former 4.7), proof revised; v4: 22pp, final version to appear in Nagoya Math. J