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

Ueda, Yoshimichi; Watatani, Yasuo

doi:10.1090/S0002-9939-99-05470-2

A relation between certain interpolated Cuntz algebras and interpolated free group factors
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by Yoshimichi Ueda and Yasuo Watatani PDF

Proc. Amer. Math. Soc. 128 (2000), 1397-1404 Request permission

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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