Classification of frobenius Lie algebras of dimension ≤ 6

Abstract

A Lie algebra g over an arbitrary field is a Frobenius Lie algebra if there is a linear form l ∈ g* whose stabilizer with respect to the coadjoint representation of g, i.e. g(l) = {X ∈ g | l([X, Y]) = 0 for all Y ∈ g} is trivial. In the present paper we classify Frobenius Lie algebras of dimension 4 over arbitrary fields of characteristic ≠ 2 and 6-dimensional Frobenius Lie algebras over algebraically closed fields of characteristic 0.