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SIGMA, 2012, Volume 8, 079, 13 pages (Mi sigma756)  

This article is cited in 3 scientific papers (total in 3 papers)

Rational Calogero–Moser model: explicit form and $r$-matrix of the second Poisson structure

Jean Avana, Eric Ragoucyb

a Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise (CNRS UMR 8089), Saint-Martin 2, 2, av. Adolphe Chauvin, F-95302 Cergy-Pontoise Cedex, France
b LAPTH Annecy le Vieux, CNRS and Université de Savoie, 9 chemin de Bellevue, BP 110, F-74941 Annecy-le-Vieux Cedex, France

Abstract: We compute the full expression of the second Poisson bracket structure for $N=2$ and $N=3$ site rational classical Calogero–Moser model. We propose an $r$-matrix formulation for $N=2$. It is identified with the classical limit of the second dynamical boundary algebra previously built by the authors.

Keywords: classical integrable systems; hierarchy of Poisson structures; dynamical reflection equation.

DOI: https://doi.org/10.3842/SIGMA.2012.079

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Full text: http://emis.mi.ras.ru/.../079
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Bibliographic databases:

ArXiv: 1207.5368
MSC: 81R12; 16T15; 16T25
Received: July 24, 2012; in final form October 17, 2012; Published online October 26, 2012
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Citation: Jean Avan, Eric Ragoucy, “Rational Calogero–Moser model: explicit form and $r$-matrix of the second Poisson structure”, SIGMA, 8 (2012), 079, 13 pp.

Citation in format AMSBIB
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\by Jean Avan, Eric Ragoucy
\paper Rational Calogero--Moser model: explicit form and $r$-matrix of the second Poisson structure
\jour SIGMA
\yr 2012
\vol 8
\papernumber 079
\totalpages 13
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Avan J., Doikou A., “The Sine-Gordon Model with Integrable Defects Revisited”, J. High Energy Phys., 2012, no. 11, 008  crossref  mathscinet  isi  scopus
    2. G. Falqui, I. Mencattini, “Bi-Hamiltonian geometry and canonical spectral coordinates for the rational Calogero–Moser system”, J. Geom. Phys., 118:SI (2017), 126–137  crossref  mathscinet  zmath  isi  scopus
    3. C. Bartocci, A. Tacchella, “Poisson–Nijenhuis structures on quiver path algebras”, Lett. Math. Phys., 107:7 (2017), 1265–1291  crossref  mathscinet  zmath  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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