Weak Centrality: AF-algebras, C(X)-algebras, and group C*-algebras
Operator Algebras
2026-01-23 v1 Functional Analysis
Abstract
We first prove that every AF-algebra is weakly central, thereby resolving a question left open by Archbold--Gogi\'c. We then establish a new characterization of weak centrality for unital -algebras in terms of -algebras. The paper concludes with an appendix that examines weak centrality in full group -algebras and places these examples within the hierarchy of group classes.
Keywords
Cite
@article{arxiv.2601.15843,
title = {Weak Centrality: AF-algebras, C(X)-algebras, and group C*-algebras},
author = {Bharat Talwar and Prahlad Vaidyanathan and Stefan Wagner},
journal= {arXiv preprint arXiv:2601.15843},
year = {2026}
}
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