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C*-Crossed-Products by an Order-Two Automorphism
Published online by Cambridge University Press: 20 November 2018
Abstract
We describe the representation theory of ${{C}^{*}}$-crossed-products of a unital
${{C}^{*}}$-algebra
$A$ by the cyclic group of order 2. We prove that there are two main types of irreducible representations for the crossed-product: those whose restriction to
$A$ is irreducible and those who are the sum of two unitarily unequivalent representations of
$A$. We characterize each class in term of the restriction of the representations to the fixed point
${{C}^{*}}$-subalgebra of
$A$. We apply our results to compute the
$K$-theory of several crossed-products of the free group on two generators.
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- Copyright © Canadian Mathematical Society 2010