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Mathematics > Quantum Algebra
Title: Tetrahedron equation and quantum cluster algebras
(Submitted on 23 Oct 2023 (v1), last revised 15 Feb 2024 (this version, v2))
Abstract: We develop the quantum cluster algebra approach recently introduced by Sun and Yagi to investigate the tetrahedron equation, a three-dimensional generalization of the Yang-Baxter equation. In the case of square quiver, we devise a new realization of quantum Y-variables in terms $q$-Weyl algebras and obtain a solution that possesses three spectral parameters. It is expressed in various forms, comprising four products of quantum dilogarithms depending on the signs in decomposing the quantum mutations into the automorphism part and the monomial part. For a specific choice of them, our formula precisely reproduces Sergeev's $R$ matrix, which corresponds to a vertex formulation of the Zamolodchikov-Bazhanov-Baxter model when $q$ is specialized to a root of unity.
Submission history
From: Rei Inoue [view email][v1] Mon, 23 Oct 2023 03:23:09 GMT (1215kb,D)
[v2] Thu, 15 Feb 2024 13:12:38 GMT (1216kb,D)
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