Spin Calogero models and dynamical r-matrices

Abstract

The main point of the construction of spin Calogero type classical integrable systems based on dynamical r-matrices, developed by L.-C. Li and P. Xu, is reviewed. It is shown that non-Abelian dynamical r-matrices with variables in a reductive Lie algebra $\mathcal{F}$ and their Abelian counterparts with variables in a Cartan subalgebra of $\mathcal{F}$ lead essentially to the same models.

Based on talk by L.F. at Symposium QTS-4, Varna (Bulgaria), August 2005; 12 pages, a remark is added and a reference is updated in v2

References in corpus (9)

• Geometry and classification of solutions of the Classical Dynamical Yang-Baxter Equation
• Classical R-matrix structure for the Calogero model
• $R$-matrices for Elliptic Calogero-Moser Models
• The R-matrix structure of the Euler-Calogero-Moser model
• Dynamical $r$-matrices for the Elliptic Calogero-Moser Model
• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• On dynamical r-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras
• Spin Calogero-Moser systems associated with simple Lie algebras
• A Class of integrable Spin Calogero-Moser systems II: Exact Solvability

Cited by in corpus (3)

• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• Superintegrability of Calogero-Moser systems associated with the cyclic quiver
• Spinning particles in a Yang-Mills field