Rocky Mountain Journal of Mathematics

The embedding of $\mathcal{O}_{d_1d_2}$ into $\mathcal{O}_{d_1}\otimes\mathcal{O}_{d_2}$

Amy B. Chambers

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Abstract

As a particular example of a general theorem presented in \cite{me}, there is a conditional expectation from the tensor product of Cuntz algebras, $\mathcal{O}_{d_1}\otimes\mathcal{O}_{d_2}$, onto the Cuntz algebra $\mathcal{O}_{d_1d_2}$. Motivated by this example, we examine the embedding of $\mathcal{O}_{d_1d_2}$ in $\mathcal{O}_{d_1}\otimes\mathcal{O}_{d_2}$, first by examining the index of the conditional expectation mentioned, and then by expressing $\mathcal{O}_{d_1}\otimes\mathcal{O}_{d_2}$ as a concrete Paschke crossed product by an endomorphism and then abstractly as the image of a faithful representation of the Stacey crossed product of $\mathcal{O}_{d_1d_2}$ by the same endomorphism.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 4 (2014), 1111-1124.

Dates
First available in Project Euclid: 31 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1414760944

Digital Object Identifier
doi:10.1216/RMJ-2014-44-4-1111

Mathematical Reviews number (MathSciNet)
MR3274339

Zentralblatt MATH identifier
1315.46056

Subjects
Primary: 46L05: General theory of $C^*$-algebras

Keywords
Graph algebra conditional exp ectation wavelet Paschke crossed product by an endomorphism Stacy crossed pro duct Cuntz algebra subalgebra

Citation

Chambers, Amy B. The embedding of $\mathcal{O}_{d_1d_2}$ into $\mathcal{O}_{d_1}\otimes\mathcal{O}_{d_2}$. Rocky Mountain J. Math. 44 (2014), no. 4, 1111--1124. doi:10.1216/RMJ-2014-44-4-1111. https://projecteuclid.org/euclid.rmjm/1414760944


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