  We consider a vector space V over K=R or C, equipped with a skew symmetric
bracket [.,.]: V x V --> V and a 2-form omega:V x V --> K. A simple change of
the Jacobi identity to the form
[A,[B,C]]+[C,[A,B]]+[B,[C,A]]=omega(B,C)A+omega(A,B)C+omega(C,A)B opens new
possibilities, which shed new light on the Bianchi classification of
3-dimensional Lie algebras.
