Approximately Finite C*-Algebras and Partial Automorphisms

TL;DR

This paper demonstrates that all approximately finite-dimensional C*-algebras can be represented as crossed products of commutative AF-algebras by partial automorphisms, with detailed analysis for UHF-algebras.

Contribution

It establishes a new structural characterization of AF-algebras as crossed products involving partial automorphisms.

Findings

Every AF-algebra is isomorphic to a crossed product of a commutative AF-algebra by a partial automorphism.

Detailed treatment of the case of UHF-algebras.

Provides a new perspective on the structure of AF-algebras.

Abstract

We prove that every AF-algebra is isomorphic to a crossed product of a commutative AF-algebra by a partial automorphism. The case of UHF-algebras is treated in detail.