Papers by Ghorbanali Haghighatdoost
Теоретическая и математическая физика, Oct 28, 2020
International Journal of Geometric Methods in Modern Physics, Jul 1, 2019
We study right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures on a Lie grou... more We study right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures on a Lie group G and introduce their infinitesimal counterpart, the so-called r-qn structures on the corresponding Lie algebra g. We investigate the procedure of the classification of such structures on the Lie algebras and then for clarity of our results we classify, up to a natural equivalence, all r-qn structures on two types of four-dimensional real Lie algebras. We mention some remarks on the relation between r-qn structures and the generalized complex structures on the Lie algebras g and also the solutions of modified Yang-Baxter equation on the double of Lie bialgebra g ⊕ g *. The results are applied to some relevant examples.
DOAJ (DOAJ: Directory of Open Access Journals), 2018
In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. ... more In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple (R, H, X) consisting of a regular multiplier Hopf algebra H, a left H-comodule algebra R, and a unital left H-module X which is also a unital algebra. First, we construct a paracyclic module to a triple (R, H, X) and then prove the existence of a cyclic structure associated to this triple.
Theoretical and Mathematical Physics, Nov 1, 2020
Using the adjoint representations of Lie algebras, we classify all Jacobi structures on real two-... more 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 low-dimensional Lie groups. Our results are illustrated through examples of Jacobi-Lie Hamiltonian systems on some real two-and three-dimensional Lie groups.
Turkish Journal of Mathematics
In the present paper we obtain sharp estimates for the squared norm of the second fundamental for... more In the present paper we obtain sharp estimates for the squared norm of the second fundamental form in terms of the mapping function for contact 3-structure CR-warped products isometrically immersed in Sasakian space form.
Communications in Mathematical Analysis, 2018
In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. ... more In this paper, we will study the theory of cyclic homology for regular multiplier Hopf algebras. We associate a cyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ consisting of a regular multiplier Hopf algebra $mathcal{H}$, a left $mathcal{H}$-comodule algebra $mathcal{R}$, and a unital left $mathcal{H}$-module $mathcal{X}$ which is also a unital algebra. First, we construct a paracyclic module to a triple $(mathcal{R},mathcal{H},mathcal{X})$ and then prove the existence of a cyclic structure associated to this triple.
Communications in Mathematical Analysis, 2020
In this work, we discuss bi-Hamiltonian structures on a family of integrable systems on 4-dimensi... more In this work, we discuss bi-Hamiltonian structures on a family of integrable systems on 4-dimensional real Lie groups. By constructing the corresponding control matrix for this family of bi-Hamiltonian structures, we obtain an explicit process for finding the variables of separation and the separated relations in detail.
Regular and Chaotic Dynamics, 2015
In 2001, A. V. Borisov, I. S. Mamaev, and V. V. Sokolov discovered a new integrable case on the L... more In 2001, A. V. Borisov, I. S. Mamaev, and V. V. Sokolov discovered a new integrable case on the Lie algebra so(4). This system coincides with the Poincaré equations on the Lie algebra so(4), which describe the motion of a body with cavities filled with an incompressible vortex fluid. Moreover, the Poincaré equations describe the motion of a four-dimensional gyroscope. In this paper topological properties of this system are studied. In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, a classification of isoenergy surfaces for this system up to the rough Liouville equivalence is obtained.
We present a short overview of Hopf algebra theory. Starting with definitions of coalgebra. bialg... more We present a short overview of Hopf algebra theory. Starting with definitions of coalgebra. bialgebra, Hopf algebra and these structures and pass to Hopf algebra symmetry and We introduce the notation, which is called Sweedler notation. In this article we introduce the afine group scheme and circular group of a Hopf algebra H.Then pass to finite Hopf algebras and Radford�s formula for S^4 and the Nichols-Zoeller theorem with proofs. Then pass to character theory for finite Hopf algebras, and finally, we introduce the class equation for Hopf algebras. and we finish this article with Hopf algebras of prime order and theorem of Zhu in 1994.
С использованием присоединенных представлений алгебр Ли проведена классификация всех структур Яко... more С использованием присоединенных представлений алгебр Ли проведена классификация всех структур Якоби на вещественных дву- и трехмерных группах Ли. Кроме того, изучены системы Якоби-Ли на таких вещественных группах Ли с небольшой размерностью. Полученные результаты иллюстрируются примерами гамильтоновых систем Якоби-Ли на некоторых вещественных дву- и трехмерных группах Ли.
Advances in Applied Clifford Algebras, 2021
This work is intended as an attempt to extend the notion of bialgebra for Lie algebras to Leibniz... more 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 is investigated. Moreover, the coboundary Leibniz bialgebras, the classical r-matrices and Yang-Baxter equations related to the Leibniz algebras are defined, and some examples are given. Finally, a method for construction of a dynamical system on a Leibniz manifold via Leibniz bialgebra is presented.
International Journal of Geometric Methods in Modern Physics, 2018
We study right-invariant (respectively, left-invariant) Poisson–Nijenhuis structures ([Formula: s... more We study right-invariant (respectively, left-invariant) Poisson–Nijenhuis structures ([Formula: see text]-[Formula: see text]) on a Lie group [Formula: see text] and introduce their infinitesimal counterpart, the so-called r-n structures on the corresponding Lie algebra [Formula: see text]. We show that [Formula: see text]-[Formula: see text] structures can be used to find compatible solutions of the classical Yang–Baxter equation (CYBE). Conversely, two compatible [Formula: see text]-matrices from which one is invertible determine an [Formula: see text]-[Formula: see text] structure. We classify, up to a natural equivalence, all [Formula: see text]-matrices and all [Formula: see text]-[Formula: see text] structures with invertible [Formula: see text] on four-dimensional symplectic real Lie algebras. The result is applied to show that a number of dynamical systems which can be constructed by [Formula: see text]-matrices on a phase space whose symmetry group is Lie group a [Formula: ...
International Journal of Geometric Methods in Modern Physics, 2019
We study right-invariant (respectively, left-invariant) Poisson quasi-Nijenhuis structures on a L... more We study right-invariant (respectively, left-invariant) Poisson quasi-Nijenhuis structures on a Lie group [Formula: see text] and introduce their infinitesimal counterpart, the so-called r-qn structures on the corresponding Lie algebra [Formula: see text]. We investigate the procedure of the classification of such structures on the Lie algebras and then for clarity of our results we classify, up to a natural equivalence, all [Formula: see text]-[Formula: see text] structures on two types of four-dimensional real Lie algebras. We mention some remarks on the relation between [Formula: see text]-[Formula: see text] structures and the generalized complex structures on the Lie algebras [Formula: see text] and also the solutions of modified Yang–Baxter equation (MYBE) on the double of Lie bialgebra [Formula: see text]. The results are applied to some relevant examples.
Teoreticheskaya i Matematicheskaya Fizika, 2017
Дана классификация всех четырехмерных действительных биалгебр Ли симплектического типа. Для этих ... more Дана классификация всех четырехмерных действительных биалгебр Ли симплектического типа. Для этих биалгебр Ли получены классические r-матрицы и структуры Пуассона на всех соответствующих четырехмерных группах Пуассона-Ли. Получены некоторые новые интегрируемые модели, для которых группа Пуассона-Ли играет роль фазового пространства, а ее дуальная группа-роль группы симметрий системы.
Journal of Nonlinear Mathematical Physics, 2021
We provide an alternative method for obtaining of compatible Poisson structures on Lie groups by ... more 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.
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Papers by Ghorbanali Haghighatdoost