Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.