On the classical \(r\)-matrix of the degenerate Calogero-Moser models

DOI10.1023/A:1022868813886zbMATH Open0979.81047arXivmath-ph/9912021OpenAlexW1607005378MaRDI QIDQ5950798

L. Fehér, B. G. Pusztai

Publication date: 17 December 2001

Published in: Czechoslovak Journal of Physics (Search for Journal in Brave)

Abstract: The most general momentum independent dynamical r-matrices are described for the standard Lax representation of the degenerate Calogero-Moser models based on $g{l}_n$ and those r-matrices whose dynamical dependence can be gauged away are selected. In the rational case, a non-dynamical r-matrix resulting from gauge transformation is given explicitly as an antisymmetric solution of the classical Yang-Baxter equation that belongs to the Frobenius subalgebra of $g{l}_n$ consisting of the matrices with vanishing last row.

Full work available at URL: https://arxiv.org/abs/math-ph/9912021

zbMATH Keywords

Lax representationdegenerate Calogero-Moser modelsmomentum independent dynamical \(r\)-matrices

Mathematics Subject Classification ID

Applications of Lie (super)algebras to physics, etc. (17B81) Many-body theory; quantum Hall effect (81V70) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (2)

Rational Calogero-Moser model: explicit form and \(r\)-matrix of the second Poisson structure ⋮ The numerical \(r\)-matrix of the elliptic Calogero-Moser model

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