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

DOI

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
@article{10_4153_CMB_2003_044_0,
     author = {Stacey, P. J.},
     title = {An {Inductive} {Limit} {Model} for the $K$ {-Theory} of the {Generator-Interchanging} {Antiautomorphism} of an {Irrational} {Rotation} {Algebra}},
     journal = {Canadian mathematical bulletin},
     pages = {441--456},
     year = {2003},
     volume = {46},
     number = {3},
     doi = {10.4153/CMB-2003-044-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-044-0/}
}
TY  - JOUR
AU  - Stacey, P. J.
TI  - An Inductive Limit Model for the $K$ -Theory of the Generator-Interchanging Antiautomorphism of an Irrational Rotation Algebra
JO  - Canadian mathematical bulletin
PY  - 2003
SP  - 441
EP  - 456
VL  - 46
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-044-0/
DO  - 10.4153/CMB-2003-044-0
ID  - 10_4153_CMB_2003_044_0
ER  - 
%0 Journal Article
%A Stacey, P. J.
%T An Inductive Limit Model for the $K$ -Theory of the Generator-Interchanging Antiautomorphism of an Irrational Rotation Algebra
%J Canadian mathematical bulletin
%D 2003
%P 441-456
%V 46
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2003-044-0/
%R 10.4153/CMB-2003-044-0
%F 10_4153_CMB_2003_044_0

Cité par Sources :