Hicham Lebzioui
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Research Subjects
Hicham Lebzioui has a total of 9 co-authors. Here are the top co-authors by number of shared publications:
Hamza El Ouali
6 shared publicationsMohamed Boucetta
4 shared publications- Saïd Benayadi
Laboratoire IECL, CNRS-UMR 7502, UFR MIM, Université de Lorraine, Metz Cedex 03, France
3 shared publications Fatima-Ezzahrae Abid
2 shared publications- Ignacio Bajo
Depto. Matemática Aplicada II, Universidade de Vigo, Vigo, Spain
2 shared publications - Mohamed Boucetta
Université Cadi-Ayyad Faculté des sciences et techniques BP 549 Marrakech Maroc
2 shared publications
Latest Publications
- Open Access
- 31 July 2026
- Published by Springer Nature in Results in Mathematics
- Vol. 81 (5) , 159
Flat Left-Invariant Lorentzian Metrics on Almost Abelian Lie Groups
Almost abelian Lie groups are those admitting a normal subgroup which is commutative and of codimension one. We determine all Lie algebras of almost abelian Lie groups admitting a left-invariant Lorentzian metric of vanishing curvature. For each of those algebras, we completely classify the set of inequivalent flat Lorentzian products.
- 31 July 2026
- Published by Springer Nature in Results in Mathematics
- Vol. 81 (5) , 159
Open AccessFlat Left-Invariant Lorentzian Metrics on Almost Abelian Lie Groups
Almost abelian Lie groups are those admitting a normal subgroup which is commutative and of codimension one. We determine all Lie algebras of almost abelian Lie groups admitting a left-invariant Lorentzian metric of vanishing curvature. For each of those algebras, we completely classify the set of inequivalent flat Lorentzian products.
- 23 June 2026
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 749, 15-37
Flat left-invariant pseudo-Riemannian metrics of index 2 on filiform Lie groups
- 23 June 2026
- Published by Elsevier in Linear Algebra and its Applications
- Vol. 749, 15-37
Flat left-invariant pseudo-Riemannian metrics of index 2 on filiform Lie groups
- 25 May 2026
- Published by Elsevier in Differential Geometry and its Applications
- Vol. 103
Cyclic Riemannian Lie groups: description and curvatures
- 25 May 2026
- Published by Elsevier in Differential Geometry and its Applications
- Vol. 103
Cyclic Riemannian Lie groups: description and curvatures
- Open Access
- 4 March 2026
- Published by Elsevier in SSRN Electronic Journal
Cyclic Riemannian Lie groups: description and curvatures
A cyclic Riemannian Lie group is a Lie group G equipped with a left-invariant Riemannian metric h that satisfies HX,Y,Z h([X,Y],Z) = 0 for any left-invariant vector fields X,Y,Z. The initial concept and exploration of these Lie groups were presented in Monatsh. Math. 176 (2015), 219239. This paper builds upon the results from the aforementioned study by providing a complete description of cyclic Riemannian Lie groups and an in-depth analysis of their various curvatures.
- 4 March 2026
- Published by Elsevier in SSRN Electronic Journal
Open AccessCyclic Riemannian Lie groups: description and curvatures
A cyclic Riemannian Lie group is a Lie group G equipped with a left-invariant Riemannian metric h that satisfies HX,Y,Z h([X,Y],Z) = 0 for any left-invariant vector fields X,Y,Z. The initial concept and exploration of these Lie groups were presented in Monatsh. Math. 176 (2015), 219239. This paper builds upon the results from the aforementioned study by providing a complete description of cyclic Riemannian Lie groups and an in-depth analysis of their various curvatures.
- Open Access
Cyclic Riemannian Lie groups: description and curvatures
A cyclic Riemannian Lie group is a Lie group $G$ equipped with a left-invariant Riemannian metric $h$ that satisfies $\oint_{X,Y,Z}h([X,Y],Z)=0$ for any left-invariant vector fields $X,Y,Z$. The initial concept and exploration of these Lie groups were presented in Monatsh. Math. \textbf{176} (2015), 219-239. This paper builds upon the results from the aforementioned study by providing a complete description of cyclic Riemannian Lie groups and an in-depth analysis of their various curvatures.Open AccessCyclic Riemannian Lie groups: description and curvatures
A cyclic Riemannian Lie group is a Lie group $G$ equipped with a left-invariant Riemannian metric $h$ that satisfies $\oint_{X,Y,Z}h([X,Y],Z)=0$ for any left-invariant vector fields $X,Y,Z$. The initial concept and exploration of these Lie groups were presented in Monatsh. Math. \textbf{176} (2015), 219-239. This paper builds upon the results from the aforementioned study by providing a complete description of cyclic Riemannian Lie groups and an in-depth analysis of their various curvatures. - 3 October 2024
- Published by Elsevier in Journal of Geometry and Physics
- Vol. 206
Pseudo-Euclidean Novikov algebras of arbitrary signature
- 3 October 2024
- Published by Elsevier in Journal of Geometry and Physics
- Vol. 206
Pseudo-Euclidean Novikov algebras of arbitrary signature
- Open Access
- 19 April 2024
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 56 (6) , 2132-2149
Classification of flat Lorentzian nilpotent Lie algebras
We give a complete classification of flat Lorentzian nilpotent Lie algebras, this is to say of pseudo‐Euclidean Lie algebras associated to nilpotent Lie groups endowed with a left‐invariant Lorentzian metric of vanishing curvature. We prove that every such a Lie algebra is a direct sum of an indecomposable flat Lorentzian Lie algebra and an abelian Euclidean summand and show that, if denotes the ‐dimensional Heisenberg Lie algebra, then the only non‐abelian Lie algebras admitting flat Lorentzian metrics which are indecomposable are and the semidirect products and , defined by some particular derivations . In all those cases we also find the equivalence classes of flat Lorentzian products.
- 19 April 2024
- Published by Wiley in Bulletin of the London Mathematical Society
- Vol. 56 (6) , 2132-2149
Open AccessClassification of flat Lorentzian nilpotent Lie algebras
We give a complete classification of flat Lorentzian nilpotent Lie algebras, this is to say of pseudo‐Euclidean Lie algebras associated to nilpotent Lie groups endowed with a left‐invariant Lorentzian metric of vanishing curvature. We prove that every such a Lie algebra is a direct sum of an indecomposable flat Lorentzian Lie algebra and an abelian Euclidean summand and show that, if denotes the ‐dimensional Heisenberg Lie algebra, then the only non‐abelian Lie algebras admitting flat Lorentzian metrics which are indecomposable are and the semidirect products and , defined by some particular derivations . In all those cases we also find the equivalence classes of flat Lorentzian products.
- 11 May 2023
- Published by Taylor & Francis in Communications in Algebra
- Vol. 51 (10) , 4382-4399
Flat symplectic Lie algebras
Let be a symplectic Lie group, i.e., a Lie group endowed with a left invariant symplectic form. If is the Lie algebra of G then we call a symplectic Lie algebra. The product on defined by extends to a left invariant connection on G which is torsion free and symplectic ( . When has vanishing curvature, we call a flat symplectic Lie group and a flat symplectic Lie algebra. In this paper, we study flat symplectic Lie groups. We start by showing that the derived ideal of a flat symplectic Lie algebra is degenerate with respect to ω. We show that a flat symplectic Lie group must be nilpotent with degenerate center. This implies that the connection of a flat symplectic Lie group is always complete. We prove that the flat symplectic double extension process can be applied to characterize all flat symplectic Lie algebras. More precisely, we show that every flat symplectic Lie algebra is obtained by a sequence of flat symplectic double extension of flat symplectic Lie algebras starting from {0}. As examples in low dimensions, we classify all flat symplectic Lie algebras of dimension .- 11 May 2023
- Published by Taylor & Francis in Communications in Algebra
- Vol. 51 (10) , 4382-4399
Flat symplectic Lie algebras
Let be a symplectic Lie group, i.e., a Lie group endowed with a left invariant symplectic form. If is the Lie algebra of G then we call a symplectic Lie algebra. The product on defined by extends to a left invariant connection on G which is torsion free and symplectic ( . When has vanishing curvature, we call a flat symplectic Lie group and a flat symplectic Lie algebra. In this paper, we study flat symplectic Lie groups. We start by showing that the derived ideal of a flat symplectic Lie algebra is degenerate with respect to ω. We show that a flat symplectic Lie group must be nilpotent with degenerate center. This implies that the connection of a flat symplectic Lie group is always complete. We prove that the flat symplectic double extension process can be applied to characterize all flat symplectic Lie algebras. More precisely, we show that every flat symplectic Lie algebra is obtained by a sequence of flat symplectic double extension of flat symplectic Lie algebras starting from {0}. As examples in low dimensions, we classify all flat symplectic Lie algebras of dimension .- Open Access
Flat symplectic Lie algebras
Let $(G,\Omega)$ be a symplectic Lie group, i.e, a Lie group endowed with a left invariant symplectic form. If $\G$ is the Lie algebra of $G$ then we call $(\G,\omega=\Om(e))$ a symplectic Lie algebra. The product $\bullet$ on $\G$ defined by $3\omega\left(x\bullet y,z\right)=\omega\left([x,y],z\right)+\omega\left([x,z],y\right)$ extends to a left invariant connection $\na$ on $G$ which is torsion free and symplectic ($\na\Om=0)$. When $\na$ has vanishing curvature, we call $(G,\Omega)$ a flat symplectic Lie group and $(\G,\om)$ a flat symplectic Lie algebra. In this paper, we study flat symplectic Lie groups. We start by showing that the derived ideal of a flat symplectic Lie algebra is degenerate with respect to $\om$. We show that a flat symplectic Lie group must be nilpotent with degenerate center. This implies that the connection $\na$ of a flat symplectic Lie group is always complete. We prove that the double extension process can be applied to characterize all flat symplectic Lie algebras. More precisely, we show that every flat symplectic Lie algebra is obtained by a sequence of double extension of flat symplectic Lie algebras starting from $\{0\}$. As examples in low dimensions, we classify all flat symplectic Lie algebras of dimension $\leq6$.Open AccessFlat symplectic Lie algebras
Let $(G,\Omega)$ be a symplectic Lie group, i.e, a Lie group endowed with a left invariant symplectic form. If $\G$ is the Lie algebra of $G$ then we call $(\G,\omega=\Om(e))$ a symplectic Lie algebra. The product $\bullet$ on $\G$ defined by $3\omega\left(x\bullet y,z\right)=\omega\left([x,y],z\right)+\omega\left([x,z],y\right)$ extends to a left invariant connection $\na$ on $G$ which is torsion free and symplectic ($\na\Om=0)$. When $\na$ has vanishing curvature, we call $(G,\Omega)$ a flat symplectic Lie group and $(\G,\om)$ a flat symplectic Lie algebra. In this paper, we study flat symplectic Lie groups. We start by showing that the derived ideal of a flat symplectic Lie algebra is degenerate with respect to $\om$. We show that a flat symplectic Lie group must be nilpotent with degenerate center. This implies that the connection $\na$ of a flat symplectic Lie group is always complete. We prove that the double extension process can be applied to characterize all flat symplectic Lie algebras. More precisely, we show that every flat symplectic Lie algebra is obtained by a sequence of double extension of flat symplectic Lie algebras starting from $\{0\}$. As examples in low dimensions, we classify all flat symplectic Lie algebras of dimension $\leq6$. - 1 December 2020
- Published by Elsevier in Journal of Algebra
- Vol. 564, 300-316
On pseudo-Euclidean Novikov algebras
- 1 December 2020
- Published by Elsevier in Journal of Algebra
- Vol. 564, 300-316
On pseudo-Euclidean Novikov algebras