Non-isomorphism of reduced free group $C^\ast$-algebras

David Gao; Srivatsav Kunnawalkam Elayavalli

doi:10.48550/arxiv.2602.09995

Non-isomorphism of reduced free group $C^\ast$-algebras

arXiv (Cornell University) 2026 Preprint Open access

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Authors: David Gao, Srivatsav Kunnawalkam Elayavalli

DOI: 10.48550/arxiv.2602.09995

Cited by: 0

Abstract

Using a new approach involving embedding spaces in II$_1$ factors with plenty of freely independent Haar unitaries, we prove that $C^\ast_r(\mathbb{F}_n)\ncong C^\ast_r(\mathbb{F}_m)$ for $n \neq m$. This recovers the seminal result of Pimsner and Voiculescu with a short new proof.

Fields of Study & Subjects

Advanced Operator Algebra Research Holomorphic and Operator Theory Advanced Banach Space Theory

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 10 February 2026
Language: EN
Document type: Preprint