Magnetic Equivariant Graded Brauer Group

TL;DR

This paper introduces the magnetic equivariant graded Brauer group, classifies its structure, and links it to twistings in magnetic equivariant K-theory, expanding understanding of algebraic structures in magnetic symmetry contexts.

Contribution

It explicitly determines the structure of the magnetic equivariant graded Brauer group and relates it to magnetic equivariant K-theory twistings.

Findings

The magnetic equivariant graded Brauer group is an explicitly determined abelian group.

Elements of this group parametrize twistings of magnetic equivariant K-theory.

The structure generalizes classical Brauer groups to magnetic symmetry settings.

Abstract

Given a magnetic finite group, we consider the similarity classes of magnetic equivariant central simple graded algebras over the complex numbers. We call this set the magnetic equivariant graded Brauer group and its structure as an abelian group is explicitly determined. Following Karoubi, we argue that the elements of this graded Brauer group parametrize the twistings of the magnetic equivariant K-theory of a point.