Liouville Integrability of a Class of Integrable Spin Calogero-Moser Systems and Exponents of Simple Lie Algebras

2010/07/22 by Luen-Chau Li, Zhaohu Nie
Chemistry · Mathematics · Physics and Astronomy · #Algebra over a field #Algebraic structures and combinatorial models #Class (philosophy) #Computer science #Integrable system #Invariant (physics) #Lax pair #Lie algebra #Lie conformal algebra #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Pure mathematics #Simple (philosophy) #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1007/s00220-011-1359-x

arxiv created 2010/07/22 · openalex publication_date 2011/10/20 · arxiv updated 2015/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

In previous work, we introduced a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter, as classified by Etingof and Varchenko for simple Lie algebras. Here the main purpose is to establish the Liouville integrability of these systems by a uniform method.

Citations

• The r-matrix structure of the Euler-Calogero-Moser model
• Interacting Fermion Systems from Two Dimensional QCD
• A Class of integrable Spin Calogero-Moser systems II: Exact Solvability
• Lie Group Representations on Polynomial Rings