arXiv subjects

J. Abedi-Fardad

Publications and source records attributed to J. Abedi-Fardad.

5 recordsLinked to original sources

arXiv2026

Classification of Six-dimensional Real Nilpotent Lie Bialgebras of Symplectic Type and their Poisson-Lie Groups

In this paper, we classify all six-dimensional real nilpotent Lie bialgebras of symplectic type. The Poisson structures on all of the related six-dimensional Poisson-Lie groups are obtained. Some new integrable Hamiltonian systems for which the Poisson-Lie group plays the role of a phase space and its dual Lie group plays the role of a symmetry group of the system are obtained.

math-ph↗

arXiv2019

Exchanging role of the phase space and symmetry group of integrable Hamiltonian systems related to Lie bialgebras of bi-symplectic types

We construct integrable Hamiltonian systems with Lie bialgebras $({\bf g} , {\bf \tilde{g}})$ of the bi-symplectic type for which the Poisson-Lie groups ${\bf G}$ play the role of the phase spaces, and their dual Lie groups ${\bf {\tilde {G}}}$ play the role of the symmetry groups of the systems. We give the new transformations to exchange the role of phase spaces and symmetry groups and obtain the relations between integrals of motions of these integrable systems. Finally, we give some examples of real four-dimensional Lie bialgebras of bi-symplectic type.

math-ph↗

arXiv2017

Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups

We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by means of the adjoint representations of Lie algebras. In this way, we calculate some compatible Poisson structures on four dimensional and nilpotent six dimensional symplectic real Lie groups. Then using Magri-Morosi's theorem we obtain new bi-Hamiltonian systems with four dimensional and nilpotent six dimensional symplectic real Lie groups as phase spaces.

math.SG↗

arXiv2017

Classification of four dimensional real Lie bialgebras of symplectic type and their Poisson-Lie groups

In this paper we classify all four dimensional real Lie bialgebras of symplectic type. The classical r- matrices for these Lie bialgebras and Poisson structures on all of the related four dimensional Poisson-Lie groups are also obtained. Some new integrable models for which the Poisson-Lie group plays the role as a phase space and its dual Lie group plays the role of a symmetry group of the system, are obtained.

math-ph↗

arXiv2014

Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems

We construct integrable and superintegrable Hamiltonian systems using the realizations of four dimensional real Lie algebras as a symmetry of the system with the phase space R4 and R6. Furthermore, we construct some integrable and superintegrable Hamiltonian systems for which the symmetry Lie group is also the phase space of the system.

math-ph↗