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

DOI:
https://doi.org/10.1090/S0002-9939-99-05470-2

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

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