This article is cited in 6 papers

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

Alina Dobrogowska, Anatol Odzijewicz

Institute of Mathematics, University of Białystok, Lipowa 41, 15-424 Białystok, Poland

Abstract: 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.

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

MSC: 70H06; 37J15; 53D17

Received: November 5, 2013; in final form May 26, 2014; Published online June 3, 2014

Language: English

DOI: 10.3842/SIGMA.2014.056

Bibliographic databases:

• 
• 
• 

ArXiv: 1311.0679