11 citations · 39 across the 12 of their papers we have counts for
12 papers
Equivariant Nijenhuis Lie Algebras: Extensions to Classical Lie-Theoretic Structures
Shuai Hou, Zohreh Ravanpak, Yunhe Sheng
We develop a theory of equivariant Nijenhuis Lie algebras (ENL algebras), namely Lie algebras equipped with Nijenhuis operators satisfying an equivariance condition with respect to…
Metric degeneracies and gradient flows on symplectic leaves
Zohreh Ravanpak, Cornelia Vizman
For a Poisson manifold endowed with a pseudo-Riemannian metric, we investigate degeneracies arising when the metric is restricted to symplectic leaves. Central to this work is the…
NL bialgebras
Zohreh Ravanpak
In this paper, we introduce the concept of (weak) NL bialgebras. These structures consist of a Lie bialgebra $(\g,[\cdot,\cdot],δ)$ equipped with a Nijenhuis structure on the Lie a…
Generalized double bracket vector fields
Petre Birtea, Zohreh Ravanpak, Cornelia Vizman
We generalize double bracket vector fields, originally defined on semisimple Lie algebras, to Poisson manifolds equipped with a pseudo-Riemannian metric by utilizing a symmetric co…
Unimodularity and invariant volume forms for Hamiltonian dynamics on Poisson-Lie groups
I. Gutierrez-Sagredo, D. Iglesias Ponte, J. C. Marrero +2
In this paper, we discuss several relations between the existence of invariant volume forms for Hamiltonian systems on Poisson-Lie groups and the unimodularity of the Poisson-Lie s…
VB-structures and generalizations
Janusz Grabowski, Katarzyna Grabowska, Zohreh Ravanpak
Motivated by properties of higher tangent lifts of geometric structures, we introduce concepts of weighted structures for various geometric objects on a manifold F equipped with a…
Nonassociative analogs of Lie groupoids
Janusz Grabowski, Zohreh Ravanpak
We introduce nonassociative geometric objects generalising naturally Lie groupoids and called (smooth) quasiloopoids and loopoids. We prove that the tangent bundles of smooth loopo…
Discrete mechanics on unitary octonions
Janusz Grabowski, Zohreh Ravanpak
In this article we generalize the discrete Lagrangian and Hamiltonian mechanics on Lie groups to non-associative objects generalizing Lie groups (smooth loops). This shows that the…
Transitive nilpotent Lie algebras of vector fields and their Tanaka prolongations
Katarzyna Grabowska, Janusz Grabowski, Zohreh Ravanpak
Transitive local Lie algebras of vector fields can be easily constructed from dilations of associating with coordinates positive weights (give me a sequence of p…
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…
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…
Poisson-Lie groups, bi-Hamiltonian systems and integrable deformations
Angel Ballesteros, Juan Carlos Marrero, Zohreh Ravanpak
Given a Lie-Poisson completely integrable bi-Hamiltonian system on , we present a method which allows us to construct, under certain conditions, a completely integrab…