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Boundaries of reduced free group C*‐algebras
Author(s) -
Ozawa Narutaka
Publication year - 2007
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bdl003
Subject(s) - mathematics , injective function , group (periodic table) , free product , envelope (radar) , pure mathematics , crossed product , product (mathematics) , boundary (topology) , group algebra , algebra over a field , free group , combinatorics , mathematical analysis , geometry , chemistry , telecommunications , radar , computer science , organic chemistry
Abstract We prove that the crossed product C*‐algebra C * r (Γ, ∂Γ) of a free group Γ with its boundary ∂Γ sits naturally between the reduced group C*‐algebra C * r Γ and its injective envelope I ( C * r Γ). In other words, we have natural inclusion C * r Γ ⊂ C * r (Γ, ∂Γ) ⊂ I ( C * r Γ) of C*‐algebras.