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

David Gao; Srivatsav Kunnawalkam Elayavalli

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

Operator Algebras 2026-02-11 v1

Authors: David Gao , Srivatsav Kunnawalkam Elayavalli

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.

Keywords

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Cite

@article{arxiv.2602.09995,
  title  = {Non-isomorphism of reduced free group $C^\ast$-algebras},
  author = {David Gao and Srivatsav Kunnawalkam Elayavalli},
  journal= {arXiv preprint arXiv:2602.09995},
  year   = {2026}
}

Comments

5 pages. Comments welcome

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