Abstract:
To deseribe the unification of the fundamental interactions of elementary particles and gravitation the graded bundle mathematical structure $\zeta$ is needed. Its base $B$ is
the 9-dimensional graded space having one scalar, four spinor and four vector dimensions.
One-parametric family of the Poincaré group $1P$ is found. It is shown that any group of this family acts on its invariant subgroup and on the base $B$ in different ways. This situation is
different from the classical one and point out at the nontriviality of the $\zeta$-bundle geometrical properties. The problem of twisting is discussed.
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