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A relation between certain interpolated Cuntz algebras and interpolated free group factors


Authors: Yoshimichi Ueda and Yasuo Watatani
Journal: Proc. Amer. Math. Soc. 128 (2000), 1397-1404
MSC (2000): Primary 46L09, 46L35, 46L54
Published electronically: September 27, 1999
MathSciNet review: 1691008
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Abstract | References | Similar Articles | Additional Information

Abstract: We investigate von Neumann algebras generated by the real parts of generators of Toeplitz extensions of interpolated Cuntz algebras $\mathcal O_{\beta}$ on sub-Fock spaces. We show that some of them are isomorphic to interpolated free group factors $L(F_r)$. For example, in case of the golden number $\beta = \frac{1+\sqrt{5}}{2}$ the corresponding number $r$ is $\frac{3}{2}$.


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Additional Information

Yoshimichi Ueda
Affiliation: Graduate School of Mathematics, Kyushu University, Fukuoka, Ropponmatsu, 810-8560, Japan
Address at time of publication: Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, 739-8526, Japan
Email: ueda@math.sci.hiroshima-u.ac.jp

Yasuo Watatani
Affiliation: Graduate School of Mathematics, Kyushu University, Fukuoka, Ropponmatsu, 810-8560, Japan
Email: watatani@math.kyushu-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-99-05470-2
Keywords: Cuntz algebra, free group factor, $\beta$-shift
Received by editor(s): June 29, 1998
Published electronically: September 27, 1999
Communicated by: David R. Larson
Article copyright: © Copyright 2000 American Mathematical Society