Automorphisms of a non-type I C*-algebra

TL;DR

This paper extends Glimm's theorem by demonstrating that a UHF algebra with a product type automorphism can be covariantly embedded into a non-type I C*-algebra with an automorphism exhibiting full Connes spectrum, revealing new structural insights.

Contribution

It provides a covariant version of Glimm's theorem, linking automorphisms with full Connes spectrum to embeddings of UHF algebras in non-type I C*-algebras.

Findings

UHF algebra with a product type automorphism can be covariantly embedded

Automorphisms with full Connes spectrum are key to the embedding

Extension of Glimm's theorem to covariant settings

Abstract

Glimm's theorem says that a UHF algebra is almost embedded in a separable $C^*$-algebra not of type I. Applying his methods we obtain a covariant version of his result; a UHF algebra with a product type automorphism is covariantly embedded in such a $C^*$-algebra equipped with an automorphism with full Connes spectrum.