Free group C^*-algebras associated with ℓ_p

2012/03/05 by Rui Okayasu, Okayasu, Rui
Mathematics · #22D25 #46L05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1203.0800

openalex publication_date 2012/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every p≥ 2, we give a characterization of positive definite functions on a free group with finitely many generators, which can be extended to the positive linear functionals on the free group C^*-algebra associated with the ideal ℓ_p. This is a generalization of Haagerup's characterization for the case of the reduced free group C^*-algebra. As a consequence, the associated C^*-algebras are mutually non-isomorphic, and they have a unique tracial state.

Related

• Pure eigenstates for the sum of generators of the free group
• Pure states on free group C*-algebras
• Free coactions of a finite dimensional C^*-Hopf algebra and strong Morita equivalence
• Strict comparison in reduced group C^*-algebras
• Freeness of actions of finite groups on C*-algebras