  The notion of Poincare gauge manifold ($G$), proposed in the context of an
(1+1) gravitational theory by Cangemi and Jackiw (D. Cangemi and R. Jackiw,
Ann. Phys. (N.Y.) 225 (1993) 229), is explored from a geometrical point of
view. First $G$ is defined for arbitrary dimensions, and in the sequence a
symplectic structure is attached to $T*G$. Treating the case of five
dimensions, a (4,1)-de Sitter space, aplications are presented studing
representations of the Poincare group in association with kinetic theory and
the Weyl operators in phase space. The central extension in the
Aghassi-Roman-Santilli group (J. J. Aghassi, P. Roman and R. M. Santilli, Phys.
Rev. D 1(1970) 2573) is derived as a subgroup of linear transformations in $G$
with six dimensions.
