Galilei Covariance and (4,1)-de Sitter Space

A vector space Q 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. 327 The context of Galilean symmetries constitute a natural setting for formulations of non-relativistic theories, with particular signficance to the study of the condensed matter physics. 1)- 6) Unlike the Poincare group, however, the representations of the Galilei group (G) have not been sufficiently developed,5) even though there is a wealth of information about non-Lorentzian physics that could benefit greately from such studies. One characteristic making such a development difficult is the intricate structure of G, characterized by eleven parameters: three spatial rotations, three spatial trans