Hamza El Ouali

• Cadi Ayyad University

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...

Let (G,Ω) 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,ω=Ω(e))a symplectic Lie algebra. The product • on g defined by 3ω(x•y,z)=ω([x,y],z)+ω([x,z],y) extends to a left invariant connection ∇ on G which is torsion free and symplectic (∇Ω=0). When ∇ has vanish...

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...