AF-embeddings of residually finite dimensional C*-algebras

TL;DR

This paper proves that certain residually finite dimensional C*-algebras with specific K-homology properties can be embedded into uniformly hyperfinite C*-algebras, advancing understanding of their structure.

Contribution

It demonstrates that separable exact residually finite dimensional C*-algebras with locally finitely generated even K-homology embed into UHF C*-algebras, a novel structural result.

Findings

Embedding of specified C*-algebras into UHF algebras

Connection between K-homology properties and algebra embeddings

Advancement in classification of residually finite dimensional C*-algebras

Abstract

It is shown that a separable exact residually finite dimensional C*-algebra with locally finitely generated (rational) even K-homology embeds in a uniformly hyperfinite C*-algebra.