11 citations · 40 across the 13 of their papers we have counts for
13 papers
Classification of Six-dimensional Real Nilpotent Lie Bialgebras of Symplectic Type and their Poisson-Lie Groups
A. Poursistani, Gh. Haghighatdoost, J. Abedi-Fardad
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…
Integrable bi-Hamiltonian systems by Jacobi structure on real three-dimensional Lie groups
H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam
By Poissonization of Jacobi structures on real three-dimensional Lie groups and using the realizations of their Lie algebras, we obtain integrable bi-Hamiltonian syste…
Poisson-Nijenhuis Structure on Lie groupoids from the Invariance's Point of View
Gh. Haghighatdoost, J. Ojbag
In this paper, we introduce right-invariant (similarly, left-invariant) Poisson-Nijenhuis Structures on Lie groupoids and their infinitesimal counterparts as called $(Λ, \mathbf{n}…
Jacobi structures on real two- and three-dimensional Lie groups and their Jacobi-Lie systems
H. Amirzadeh-Fard, Gh. Haghighatdoost, P. Kheradmandynia +1
Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two- and three-dimensional Lie groups. Also, we study Jacobi-Lie systems on these real…
Jacobi-Lie Hamiltonian systems on real low-dimensional Jacobi-Lie groups and their Lie symmetries
H. Amirzadeh-Fard, Gh. Haghighatdoost, A. Rezaei-Aghdam
We study Jacobi-Lie Hamiltonian systems admitting Vessiot-Guldberg Lie algebras of Hamiltonian vector fields related to Jacobi structures on real low-dimensional Jacobi-Lie groups.…
Generalized geometric Hamilton-Jacobi theorem on Lie algebroids
Gh. Haghighatdoost, R. Ayoubi
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system on Lie algebroids are given. Here we use the general properties of Lie algebroids to express…
Some remarks on invariant Poisson quasi-Nijenhuis structures on Lie groups
Ghorbanali Haghighatdoost, Zohreh Ravanpak, Adel Rezaei-Aghdam
We study {\em right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures} on a Lie group and introduce their infinitesimal counterpart, the so-called {\em r-qn…
Exchanging role of the phase space and symmetry group of integrable Hamiltonian systems related to Lie bialgebras of bi-symplectic types
J. Abedi-Fardad, A. Rezaei-Aghdam, Gh. Haghighatdoost
We construct integrable Hamiltonian systems with Lie bialgebras of the bi-symplectic type for which the Poisson-Lie groups play the role of…
On bi-Hamiltonian structure of some superintegrable systems
Gh. Haghighatdoost, S. Abdolhadi-zangakani
We discuss bi-Hamiltonian structures for integrable and superintegrable Hamiltonian system on the list of symplectic four-dimensional real Lie groups are classified by G. Ovando. I…
Invariant Poisson-Nijenhuis structures on Lie groups and classification
Zohreh Ravanpak, Adel Rezaei-Aghdam, Ghorbanali Haghighatdoost
We study right-invariant (resp., left-invariant) Poisson-Nijenhuis structures on a Lie group and introduce their infinitesimal counterpart, the so-called r-n structures on the…
Some compatible Poisson structures and integrable bi-Hamiltonian systems on four dimensional and nilpotent six dimensional symplectic real Lie groups
J. Abedi-Fardad, A. Rezaei-Aghdam, Gh. Haghighatdoost
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 som…
Leibniz bialgebras, classical Yang-Baxter equations and dynamical systems
A. Rezaei-Aghdam, L. Sedghi-Ghadim, GH. Haghighatdoost
This work is intended as an attempt to extend the notion of bialgebra for Lie algebras to Leibniz algebras and also, the correspondence between the Leibniz bialgebras and its dual…
Integrable and superintegrable Hamiltonian systems with four dimensional real Lie algebras as symmetry of the systems
J. Abedi-Fardad, A. Rezaei-Aghdam, Gh. Haghighatdoost
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…