Corestriction for algebras with group action

TL;DR

This paper introduces a corestriction map for equivariant Brauer groups, generalizing existing concepts and demonstrating properties analogous to those in group cohomology, especially Galois cohomology.

Contribution

It defines a new corestriction map for equivariant Brauer groups, extending the framework of Brauer-Clifford groups and establishing its key properties.

Findings

Corestriction map behaves similarly to that in Galois cohomology.

Composition of corestriction and restriction relates to subgroup index.

Generalizes existing Brauer group concepts.

Abstract

We define a corestriction map for equivariant Brauer groups in the sense of Fr\"ohlich and Wall, which contain as a special case the Brauer-Clifford groups introduced by Turull. We show that this corestriction map has similar properties as the corestriction map in group cohomology (especially Galois cohomology). In particular, composing corestriction and restriction associated to a subgroup $H\leq G$ amounts to powering with the index $\lvert G:H \rvert$.