Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 056, 18 pages      arXiv:1311.0679

Integrable Systems Related to Deformed $\mathfrak{so}(5)$

Alina Dobrogowska and Anatol Odzijewicz
Institute of Mathematics, University of Białystok, Lipowa 41, 15-424 Białystok, Poland

Received November 05, 2013, in final form May 26, 2014; Published online June 03, 2014

We investigate a family of integrable Hamiltonian systems on Lie-Poisson spaces $\mathcal{L}_+(5)$ dual to Lie algebras $\mathfrak{so}_{\lambda, \alpha}(5)$ being two-parameter deformations of $\mathfrak{so}(5)$. We integrate corresponding Hamiltonian equations on $\mathcal{L}_+(5)$ and $T^*\mathbb{R}^5$ by quadratures as well as discuss their possible physical interpretation.

Key words: integrable Hamiltonian systems; Casimir functions; Lie algebra deformation; symplectic dual pair; momentum map.

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