The transverse structure of Lie flows of codimension 3

Abstract

Abstract. This paper deals with the problem of the realization of a given Lie algebra as transverse algebra to a Lie foliation on a compact manifold. This is closely related to the change problem, that is to know which non-isomorphic Lie algebras can appear as transverse algebras of a given Lie foliation. We study these two problems here given a complete classification for the case of Lie flows of codimension 3. That closes the open questions stated in [GR91] and completes the work made in [HLR96].