Traces, Unitary Characters and Crossed Products by $ℤ$

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  • Traces, Unitary Characters and Crossed Products by \mathbb{Z}

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We determine the character group of the infinite unitary group of a unital exact C*-algebra in terms of K-theory and traces and obtain a description of the infinite unitary group modulo the closure of its commutator subgroup by the same means. The methods are then used to decide when the state space SK0(A×α\mathbb{Z}) of the K0 group of a crossed product by \mathbb{Z} is homeomorphic to SK0(A)α. or T(A)α. We also consider the crossed product A×αG discrete countable abelian group G and give necessary and sufficient conditions for the equality T(A×αG)=T(A)α to hold.

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