Geodesic
An Inductive Limit Model for the $K$ -Theory of the Generator-Interchanging Antiautomorphism of an Irrational Rotation Algebra
Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 441-456

Voir la notice de l'article provenant de la source Cambridge University Press

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 ${{R}_{\theta }}$ .
DOI : 10.4153/CMB-2003-044-0
Mots-clés : 46L35, 46L80 
Stacey, P. J. An Inductive Limit Model for the $K$ -Theory of the Generator-Interchanging Antiautomorphism of an Irrational Rotation Algebra. Canadian mathematical bulletin, Tome 46 (2003) no. 3, pp. 441-456. doi: 10.4153/CMB-2003-044-0
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