AN OUTER ADMISSIBLE ACTION OF A COMMUTATIVE LOCALLY COMPACT GROUP ON THE GENERIC DYNAMICS FACTOR

The generic dynamics factor is a small, monotone complete, hyperfinite wild factor of Type III obtained as a quotient of the Borel *-envelope of the Fermion algebra. In our earlier work with Wright, we constructed infinitely many outer actions of any Polish group equipped with a dense normal subgroup on. These results are algebraic and in another work with Wright, we constructed an outer admissible action of the additive group ℝ of real numbers and the torus on. Let G be any locally compact second countable commutative Hausdorff group. In this paper, we shall show that there exists an appropriate parameterization, for, that makes it possible to generalize the results of the works above, and to construct an admissible outer action of G on. When an action α of G on; is admissible, we can define the small monotone cross product α G and the dual action a of Ĝ in such a way that, the Takesaki's duality principle holds true and this is a new parameterization of the algebra.