Dilogarithm identities in cluster scattering diagrams
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866911947172085760 |
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| author | Nakanishi, Tomoki |
| author_facet | Nakanishi, Tomoki |
| contents | We extend the notion of $y$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_09555 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dilogarithm identities in cluster scattering diagrams Nakanishi, Tomoki Combinatorics Quantum Algebra We extend the notion of $y$-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. |
| title | Dilogarithm identities in cluster scattering diagrams |
| topic | Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2111.09555 |