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Crossed products by Z of algebras arising from reduced free group C *‐algebras
Author(s) -
Rada Catalin
Publication year - 2011
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/bdq093
Subject(s) - mathematics , automorphism , projection (relational algebra) , subspace topology , combinatorics , free group , group (periodic table) , automorphism group , algebra over a field , pure mathematics , chemistry , mathematical analysis , organic chemistry , algorithm
Assume that Γ is a free group on n generators g 1 , g 2 , …, g n , where 2 ⩽ n < ∞. Let Γ′ + be the subset{ g i 1m 1 g i 2m 2 … g i km k ∊ Γ | k , m 1 , … , m k ∊ N } ∪ { e } , and let P + ′ be the projection onto the subspace l 2 (Γ + ′) of l 2 (Γ). Every character χ of Γ induces an automorphism on C *‐algebra C r * (Γ, P + ′) generated by the reduced group C *‐algebra C r * (Γ) and the projection P + ′. We study the classification of the C *‐algebra crossed productsC r * ( Γ , P ′ + ) ⋊ α χ Z , where α χ is the automorphism associated to χ .