A Galileian formulation of spin. I. Clifford algebras and spin groups

By generalizing the concept of spin group to the case where the underlying orthogonal space is degenerate, the spin group associated with the homogeneous Galilei group is calculated. In so doing, the Galilei group and its spin group are clearly displayed as stability subgroups of the de Sitter group and its spin group. A notion of Clifford algebra contraction is introduced in the physical (Galilei) case and its relation to Lie algebra contraction is explored. Both the stated generalization of spin group to cases with degenerate bilinear form and the idea of Clifford algebra contraction appear to be new.