Publications of the Research Institute for Mathematical Sciences
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Traces, Unitary Characters and Crossed Products by ℤKlaus Thomsen (1) Matematisk Institute, Aarhus University, Ny Munkegade, 8000, AARHUS C, DENMARK
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 x ℤ) of the K0 group of a crossed product by ℤ is homeomorphic to SK0(A)α* or T(A)α*. We also consider the crossed product A x αG by a discrete countable abelian group G and give necessary and sufficient conditions for the equality T(A x αG) = T(A)α to hold.
Thomsen Klaus: Traces, Unitary Characters and Crossed Products by ℤ. Publ. Res. Inst. Math. Sci. 31 (1995), 1011-1029. doi: 10.2977/prims/1195163594