Hamiltonian and Lagrangian formalisms of mutations in cluster algebras and application to dilogarithm identities
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| Format: | Preprint |
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2016
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| _version_ | 1866911947108122624 |
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| author | Gekhtman, Michael Nakanishi, Tomoki Rupel, Dylan |
| author_facet | Gekhtman, Michael Nakanishi, Tomoki Rupel, Dylan |
| contents | We introduce and study a Hamiltonian formalism of mutations in cluster algebras using canonical variables, where the Hamiltonian is given by the Euler dilogarithm. The corresponding Lagrangian, restricted to a certain subspace of the phase space, coincides with the Rogers dilogarithm. As an application, we show how the dilogarithm identity associated with a period of mutations in a cluster algebra arises from the Hamiltonian/Lagrangian point of view. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1611_02813 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Hamiltonian and Lagrangian formalisms of mutations in cluster algebras and application to dilogarithm identities Gekhtman, Michael Nakanishi, Tomoki Rupel, Dylan Rings and Algebras Quantum Algebra 13F60 (Primary), 33E20 (Secondary) We introduce and study a Hamiltonian formalism of mutations in cluster algebras using canonical variables, where the Hamiltonian is given by the Euler dilogarithm. The corresponding Lagrangian, restricted to a certain subspace of the phase space, coincides with the Rogers dilogarithm. As an application, we show how the dilogarithm identity associated with a period of mutations in a cluster algebra arises from the Hamiltonian/Lagrangian point of view. |
| title | Hamiltonian and Lagrangian formalisms of mutations in cluster algebras and application to dilogarithm identities |
| topic | Rings and Algebras Quantum Algebra 13F60 (Primary), 33E20 (Secondary) |
| url | https://arxiv.org/abs/1611.02813 |