# Lie algebra associated to a linear form

Let $F$ be a finite dimensional vector space over a field $k$, if $f : F \to k$ is any linear form, I can define on $F$ a Lie algebra bracket by the following rule $$[x,y]=f(x)y-f(y)x,$$ or in terms of structure constants $$c_{ij}^k=f_i \delta_j^k-f_j\delta^k_i.$$ What is known about such algebras? Do they have a special name?

Update: in fact it is silly and trivial class of examples. Take $K$ to be kernel of $f$ then it is an abelian subalgebra, quotient $F/K$ is one dimensional and thus again abelian, it is easy to see that given algebra is a semidirect product of this two abelian algebras.

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