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An Inductive Limit Model for the $K$-Theory of the Generator-Interchanging Antiautomorphism of an Irrational Rotation Algebra

  Published:2003-09-01
 Printed: Sep 2003
  • P. J. Stacey
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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 $R_\theta$.
MSC Classifications: 46L35, 46L80 show english descriptions Classifications of $C^*$-algebras
$K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
46L35 - Classifications of $C^*$-algebras
46L80 - $K$-theory and operator algebras (including cyclic theory) [See also 18F25, 19Kxx, 46M20, 55Rxx, 58J22]
 

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