  Geometrical applications of the non-compact form of Cartan's exceptional Lie
group G(2) is considered. This group generates specific rotations of
7-dimensional Minkowski-like space with three extra time-like coordinates and
in some limiting cases imitates standard Poincare transformations. In this
model space-time translations are non-commutative and are represented by the
rotations towards the extra time-like coordinates. The second order Casimir
element of non-compact G(2) and its expression by the Casimir operators of the
Lorentz and Poincare groups are found.
