Galilei covariance and (4,1)-de Sitter space

Abstract

A vector space G is introduced such that the Galilei transformations are considered linear mappings in this manifold. The covariant structure of the Galilei Group (Y. Takahashi, Fortschr. Phys. 36 (1988), 63, 83) is derived and the tensor analysis is developed. It is shown that the Euclidean space is embedded in the (4,1)-de Sitter space through G. This is an interesting and useful property, in particular, for the analysis carried out for the Lie algebra of the generators of linear transformations in G.