9 papers
Three-Dimensional Real Affine Lie Groups
T. Aït Aissa, S. El Bourkadi, M. W. Mansouri
We classify all left-invariant real affine connections in dimension three. Our approach reduces the three-dimensional problem to a two-dimensional one by decomposing each left-inva…
Eight-Dimensional Symplectic Nilpotent Lie Groups with Lagrangian Normal Subgroups: A Complete Classification
T. Aït Aissa, M. W. Mansouri
We investigate symplectic nilpotent Lie groups with Lagrangian normal subgroups. We show that there exists a bijection between the isomorphism classes of nilpotent Lie groups with…
Eight-dimensional non completely reducible symplectic Lie algebras
T. Aït Aissa, S. El Bourkadi, M. W. Mansouri +1
A non completely reducible symplectic Lie algebra is a symplectic Lie algebra which cannot be symplectically reduced to the trivial symplectic Lie algebra. Our aim is to provide a…
On solvable complete symplectic Lie algebras
M. Benyoussef, M. W. Mansouri, SM. Sbai
In this paper, we are interested in solvable complete Lie algebras, over the field $\K=\R$ or , which admit a symplectic structure. Specifically, important classes are…
Cosymplectic Jacobi-Jordan Algebras
S. El bourkadi, M. W. Mansouri
We introduce the notion of cosymplectic structure on Jacobi-Jordan algebras, and we state that they are related to symplectic Jacobi-Jordan algebras. We show, in particular, that t…
A complete classification of symplectic forms on six-dimensional Frobeniusian real Lie algebras
T. Aït Aissa, S. Elbourkadi, M. W. Mansouri
In this paper, we give a complete classification of symplectic structures on six-dimensional Frobeniusian solvable Lie algebras, up to symplectomorphism. We provide a scheme to cla…
Eight-dimensional symplectic non-solvable Lie algebras
T. Aït Aissa, M. W. Mansouri
In this paper, we classify eight-dimensional non-solvable Lie algebras that support a symplectic structure. As well as a complete classification is given, up to symplectomorphism,…
On cosymplectic Lie Algebras
S. El bourkadi, M. W. Mansouri
We give some properties of cosymplectic Lie algebras, we show, in particular, that they support a left symmetric product. We also give some constructions of cosymplectic Lie algebr…
The classification of left-invariant para-Kähler structures on simply connected four-dimensional Lie groups
Wadia Mansouri, Ahmad Oufkou
We give a complete classification of left invariant para-Kähler structures on four-dimensional simply connected Lie groups up to an automorphism. As an application we discuss some…