J. Avan, O. Babelon, M. Talon, “Construction of the classical $R$-matrices for the Toda and Calogero models”, Algebra i Analiz, 6:2 (1994), 67–89; St. Petersburg Math. J., 6:2 (1995), 255

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Algebra i Analiz, 1994, Volume 6, Issue 2, Pages 67–89 (Mi aa436)

This article is cited in 10 scientific papers (total in 10 papers)

Research Papers

Construction of the classical

$R$ -matrices for the Toda and Calogero models

J. Avan, O. Babelon, M. Talon

L.RT.H.E. Université Paris VI (CNRS UA 280)

Full-text PDF (1897 kB) Citations (10)

Abstract: We use the definition of the Calogero–Moser models as Hamiltonian reductions of geodesic motions on a group manifold to construct their

$R$ -matrices. In the Toda case, the analogous construction yields constant

$R$ -matrices. By contrast, for Calogero–Moser models they are dynamical objects.

Received: 26.09.1993

Bibliographic databases:

Document Type: Article

Language: English

Citation: J. Avan, O. Babelon, M. Talon, “Construction of the classical

$R$ -matrices for the Toda and Calogero models”, Algebra i Analiz, 6:2 (1994), 67–89; St. Petersburg Math. J., 6:2 (1995), 255–274

Citation in format AMSBIB

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\by J.~Avan, O.~Babelon, M.~Talon

\paper Construction of the classical $R$-matrices for the Toda and Calogero models

\jour Algebra i Analiz

\yr 1994

\vol 6

\issue 2

\pages 67--89

\mathnet{http://mi.mathnet.ru/aa436}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1290819}

\zmath{https://zbmath.org/?q=an:0824.58028|0820.58028}

\transl

\jour St. Petersburg Math. J.

\yr 1995

\vol 6

\issue 2

\pages 255--274

Linking options:

https://www.mathnet.ru/eng/aa436

https://www.mathnet.ru/eng/aa/v6/i2/p67

This publication is cited in the following 10 articles:

Pusztai B.G., “on the Classical R-Matrix Structure of the Rational Bcn Ruijsenaars-Schneider-Van Diejen System”, Nucl. Phys. B, 900 (2015), 115–146
Jean Avan, Eric Ragoucy, “Rational Calogero–Moser model: explicit form and $r$-matrix of the second Poisson structure”, SIGMA, 8 (2012), 079, 13 pp.
A. V. Zotov, A. M. Levin, “Integrable Model of Interacting Elliptic Tops”, Theoret. and Math. Phys., 146:1 (2006), 45–52
Fring, A, “Non-crystallographic reduction of generalized Calogero–Moser models”, Journal of Physics A-Mathematical and General, 39:5 (2006), 1115
Alekseevsky, D, “The Riemannian geometry of orbit spaces - the metric, geodesics, and integrable systems”, Publicationes Mathematicae-Debrecen, 62:3–4 (2003), 247
Braden, HW, “Classical r-matrices and the Feigin-Odesskii algebra via Hamiltonian and Poisson reductions”, Journal of Physics A-Mathematical and General, 36:25 (2003), 6979
Feher, L, “The non-dynamical r-matrices of the degenerate Calogero–Moser models”, Journal of Physics A-Mathematical and General, 33:43 (2000), 7739
Bangoura, M, “The classical dynamical Yang–Baxter equation and Lie algebroids”, Comptes Rendus de l Academie Des Sciences Serie i-Mathematique, 327:6 (1998), 541
G. E. Arutyunov, S. A. Frolov, L. O. Chekhov, “$R$-matrix quantization of the elliptic Ruijsenaars–Schneider model”, Theoret. and Math. Phys., 111:2 (1997), 536–562
G. E. Arutyunov, “Construction of trigonometric Toda $r$-matrices via Hamiltonian reduction of the cotangent bundle over loop groups”, Theoret. and Math. Phys., 113:1 (1997), 1209–1216

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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