Tetrahedron equation and quantum cluster algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910331891089408 |
|---|---|
| author | Inoue, Rei Kuniba, Atsuo Terashima, Yuji |
| author_facet | Inoue, Rei Kuniba, Atsuo Terashima, Yuji |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14529 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Tetrahedron equation and quantum cluster algebras Inoue, Rei Kuniba, Atsuo Terashima, Yuji Quantum Algebra High Energy Physics - Theory Mathematical Physics Geometric Topology Exactly Solvable and Integrable Systems 82B23, 81R12, 13F60 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. |
| title | Tetrahedron equation and quantum cluster algebras |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Geometric Topology Exactly Solvable and Integrable Systems 82B23, 81R12, 13F60 |
| url | https://arxiv.org/abs/2310.14529 |