Bracelets bases are theta bases
The skein algebra of a marked surface, possibly with punctures, admits the basis of (tagged)
bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a …
bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a …
Pentagon relation in quantum cluster scattering diagrams
T Nakanishi - arXiv preprint arXiv:2202.01588, 2022 - arxiv.org
We formulate the pentagon relation for quantum dilogarithm elements in the structure group
of a quantum cluster scattering diagram (QCSD). As an application, we show the …
of a quantum cluster scattering diagram (QCSD). As an application, we show the …
Cluster Algebras and Dilogarithm Identities
T Nakanishi - arXiv preprint arXiv:2407.06668, 2024 - arxiv.org
This is a reasonably self-contained exposition of the fascinating interplay between cluster
algebras and the dilogarithm in the recent two decades. The dilogarithm has a long and rich …
algebras and the dilogarithm in the recent two decades. The dilogarithm has a long and rich …
Dilogarithm identities in cluster scattering diagrams
T Nakanishi - Nagoya Mathematical Journal, 2024 - cambridge.org
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 …
diagrams (CSDs). Accordingly, we extend the dilogarithm identity associated with a period in …
Skein and cluster algebras with coefficients for unpunctured surfaces
We propose a skein model for the quantum cluster algebras of surface type with coefficients.
We introduce a skein algebra $\mathscr {S} _ {\Sigma,\mathbb {W}}^{A} $ of a walled surface …
We introduce a skein algebra $\mathscr {S} _ {\Sigma,\mathbb {W}}^{A} $ of a walled surface …