Non-degenerate Invariant Bilinear Forms on Leibniz Algebras ⁄

In this paper, we study Leibniz algebras $\mathfrak{g}$ with a non-degenerate Leibniz-symmetric $\mathfrak{g}$-invariant bilinear form B, such a pair $(\mathfrak{g},B)$ is called a quadratic Leibniz algebra. Our first result generalizes the notion of double extensions to quadratic Leibniz algebras. This notion was introduced by Medina and Revoy to study quadratic Lie algebras. In the second theorem, we give a sufficient condition for a quadratic Leibniz algebra to be a quadratic Leibniz algebra by double extension.