Pentagon relation in quantum cluster scattering diagrams
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2022
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866913454320779264 |
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| author | Nakanishi, Tomoki |
| author_facet | Nakanishi, Tomoki |
| contents | 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 nonpositivity of a certain class of nonskew-symmetric QCSDs. Also, we explicitly present various consistency relations for QCSDs of rank 2 completely or up to some degree, many of which are new in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_01588 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pentagon relation in quantum cluster scattering diagrams Nakanishi, Tomoki Combinatorics Quantum Algebra 13F60 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 nonpositivity of a certain class of nonskew-symmetric QCSDs. Also, we explicitly present various consistency relations for QCSDs of rank 2 completely or up to some degree, many of which are new in the literature. |
| title | Pentagon relation in quantum cluster scattering diagrams |
| topic | Combinatorics Quantum Algebra 13F60 |
| url | https://arxiv.org/abs/2202.01588 |