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

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 $T^{\ast }{\mathbb{R}}^5$ by quadratures as well as discuss their possible physical interpretation.

References in corpus (3)

• Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal
• Hierarchy of integrable Hamiltonians describing of nonlinear n-wave interaction
• Integrable relativistic systems given by Hamiltonians with momentum-spin-orbit coupling

Cited by in corpus (1)

• Lie bundle on the space of deformed skew-symmetric matrices