In this paper we construct a Chern-Weil isomorphism for the equivariant Brauer group of R^n-actions on a principal torus bundle, where the target for this isomorphism is a dimensionally reduced Cech cohomology group. From this point of view, the usua
l forgetful functor takes the form of a connecting homomorphism in a long exact sequence in dimensionally reduced cohomology.
In this paper we outline a recent construction of a Chern-Weil isomorphism for the equivariant Brauer group of $mathbb R^n$ actions on a principal torus bundle, where the target for this isomorphism is a dimensionally reduced vCech cohomology group.
Using this latter group, we demonstrate how to extend the induced algebra construction to algebras with a non-trivial bundle as their spectrum.
