Rational magnetic equivariant K-theory

TL;DR

This paper introduces magnetic equivariant K-theory groups, establishing a rational isomorphism with conjugation-invariant parts of complex equivariant K-theory, simplifying calculations of these groups.

Contribution

It defines magnetic equivariant K-theory and proves a rational isomorphism to known complex equivariant K-theory, enabling easier computation.

Findings

Established the magnetic equivariant K-theory groups.

Proved a rational isomorphism with conjugation-invariant complex equivariant K-theory.

Simplified the calculation of torsion-free parts of magnetic equivariant K-theory.

Abstract

We introduce the magnetic equivariant K-theory groups as the K-theory groups associated to magnetic groups and their respective magnetic equivariant complex bundles. We restrict the magnetic group to its subgroup of elements that act complex linearly, and we show that this restriction induces a rational isomorphism with the conjugation invariant part of the complex equivariant K-theory of the restricted group. This isomorphism allows to calculate the torsion free part of the magnetic equivariant K-theory groups reducing it to known calculations in complex equivariant K-theory