%0 Journal Article
%T Classification of homogeneous CR-manifolds in dimension 4
%A V. K. Beloshapka
%A I. G. Kossovskiy
%J Mathematics
%D 2009
%I arXiv
%X Locally homogeneous CR-manifolds in dimension 3 were classified, up to local CR-equivalence, by E.Cartan. We classify, up to local CR-equivalence, all locally homogeneous CR-manifolds in dimension 4. The classification theorem enables us also to classify all symmetric CR-manifolds in dimension 4, up to local biholomorphic equivalence. We also prove that any 4-dimensional real Lie algebra can be realized as an algebra of affine vector fields in a domain in $\CC{3}$, linearly independent at each point.
%U http://arxiv.org/abs/0911.1167v3