2006/05/31 by Pawel Nurowski · 1 citation
Mathematics · #math.DG
paper · pdf · doi:10.1016/j.geomphys.2006.10.008
An error consisting in overlooking few types in the Bianchi classification is corrected
arxiv created 2006/06/12 · arxiv updated 2009/12/01
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.