# Traces, Unitary Characters and Crossed Products by ℤ

### Klaus Thomsen

Aarhus University, Denmark

## Abstract

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 _SK_0(*A* x ℤ) of the *K_0 group of a crossed product by ℤ is homeomorphic to SK_0(A)α* or T(A)α*. We also consider the crossed product A x α_G by a discrete countable abelian group G and give necessary and sufficient conditions for the equality T(A x α_G*) =

*T*(

*A*)α to hold.

## Cite this article

Klaus Thomsen, Traces, Unitary Characters and Crossed Products by ℤ. Publ. Res. Inst. Math. Sci. 31 (1995), no. 6, pp. 1011–1029

DOI 10.2977/PRIMS/1195163594