Contact transformations. IV. Contraction of contact Lie algebras

Abstract

Conventional Lie algebra contraction is envisaged as a particular case where the correspondent vector fields defining infinitesimal generators of the transformations are vector fields over a differentiable manifold. More general vector fields over tangent space are considered as infinitesimal generators of contact transformations building up a Lie algebra. A new contraction procedure is defined over such vector fields by means of a Taylor expansion. The most striking feature is that the global structure of Lie algebra remains unchanged, while the individual structure of generators is changed.