Recent advances in the study of the Equivariant Brauer Group

TL;DR

This paper presents a new Chern-Weil isomorphism for the equivariant Brauer group of a0a0a0a0 actions on principal torus bundles, linking it to a dimensionally reduced a9a9a9 cohomology, and extends algebra constructions to non-trivial bundles.

Contribution

It introduces a novel Chern-Weil isomorphism for the equivariant Brauer group and extends algebra constructions to non-trivial bundle spectra.

Findings

Established a Chern-Weil isomorphism for a0a0a0a0 actions on principal torus bundles.

Connected the isomorphism to a dimensionally reduced a9a9a9 cohomology group.

Extended the induced algebra construction to algebras with non-trivial bundle spectra.

Abstract

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.