The Hamiltonian systems on the Poisson structure of the quasi-classical limit of \(GL_ q(\infty{})\) (Q1182297)
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scientific article; zbMATH DE number 30790
| Language | Label | Description | Also known as |
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| English | The Hamiltonian systems on the Poisson structure of the quasi-classical limit of \(GL_ q(\infty{})\) |
scientific article; zbMATH DE number 30790 |
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The Hamiltonian systems on the Poisson structure of the quasi-classical limit of \(GL_ q(\infty{})\) (English)
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28 June 1992
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This paper considers the Poisson algebra introduced by \textit{B. A. Kupershmidt} on the coordinate ring of \(GL(\infty)\) [in Mechanics, Analysis and Geometry: 200 years after Lagrange, 171-199 (1991; Zbl 0726.17017)] as a quasi-classical limit of the coordinate ring of the quantum group \(GL_ p(\infty)\). The symmetrized version of this Poisson algebra is shown to give the Toda lattice equations.
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Poisson algebra
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coordinate ring
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quantum group
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Toda lattice
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