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

Published online by Cambridge University Press:  20 November 2018

P. J. Stacey
P. J. Stacey*
Affiliation:
Department of Mathematics La Trobe University Victoria 3086 Australia, e-mail: [email protected]
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Abstract

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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 ${{R}_{\theta }}$.

Keywords

46L3546L80
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 3 , 01 September 2003 , pp. 441 - 456
Copyright
Copyright © Canadian Mathematical Society 2003

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