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An Inductive Limit Model for the $K$Theory of the GeneratorInterchanging Antiautomorphism of an Irrational Rotation Algebra


Published:20030901
Printed: Sep 2003
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Abstract
Let $A_\theta$ be the universal $C^*$algebra generated by two
unitaries $U$, $V$ satisfying $VU=e^{2\pi i\theta} UV$ and let $\Phi$
be the antiautomorphism of $A_\theta$ interchanging $U$ and $V$. The
$K$theory of $R_\theta=\{a\in A_\theta:\Phi(a)=a^*\}$ is computed. When
$\theta$ is irrational, an inductive limit of algebras of the form
$M_q(C(\mathbb{T})) \oplus M_{q'} (\mathbb{R}) \oplus M_q(\mathbb{R})$
is constructed which has complexification $A_\theta$ and the same
$K$theory as $R_\theta$.