On Equivariant Embedding of Hilbert C^* modules

TL;DR

This paper proves that any Hilbert G-C*-module over an ergodic action of a compact Lie group can be embedded into a trivial module, extending the understanding of equivariant embeddings in operator algebras.

Contribution

It establishes the existence of equivariant embeddings for all Hilbert G-C*-modules under ergodic actions of compact Lie groups, regardless of countable generation.

Findings

Any Hilbert G-C*-module admits an equivariant embedding into a trivial module.

The result applies to modules over ergodic actions of compact Lie groups.

It generalizes previous results to non-countably generated modules.

Abstract

We prove that an arbitrary (not necessarily countably generated) Hilbert $G$-$\cla$ module on a G-C^* algebra $\cla$ admits an equivariant embedding into a trivial $G-\cla$ module, provided G is a compact Lie group and its action on $\cla$ is ergodic.