On continuous fiber bundles of C*-algebras over Stonean compact

TL;DR

This paper introduces a new class of C*-algebras over Stonean compact spaces, representing them as continuous fiber bundles of C*-algebras, thus extending the understanding of their structure in a topological setting.

Contribution

It defines C*-algebras over C_{ ext{infty}}(Q,C) and proves their unique representation as continuous fiber bundles over Stonean compact Q.

Findings

C*-algebras over C_{ ext{infty}}(Q,C) are characterized as Banach-Kantorovich *-algebras.

Such algebras can be uniquely represented by continuous fiber bundles of C*-algebras.

The representation is up to a Q-C*-isomorphism.

Abstract

We introduce C*-algebras over C_{\infty}(Q,C) as Banach-Kantorovich *-algebras over the algebra C_{\infty}(Q,C) of extended continuous complex-valued functions, defined on comeager subsets of Stonean compact Q, whose norm satisfies conditions similar to the axioms of C*-algebras, and show that such algebras can be uniquely up to a Q-C*-isomorphism represented by means of a continuous complete fiber bundle of C*-algebras over Q.