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Free group C*-algebras associated with ℓ_p

Rui Okayasu

Department of Mathematics Education, Osaka Kyoiku University, 4-698-1 Asahigaoka, Kashiwara, Osaka 582-8582, Japan

https://doi.org/10.1142/S0129167X14500657Cited by:19 (Source: Crossref)

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 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 canonical quotient map between the associated C*-algebras is not injective, and they have a unique tracial state.

Keywords:

AMSC: 46L05, 22D25

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