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.
Citation
Amy B. Chambers. "The embedding of $\mathcal{O}_{d_1d_2}$ into $\mathcal{O}_{d_1}\otimes\mathcal{O}_{d_2}$." Rocky Mountain J. Math. 44 (4) 1111 - 1124, 2014. https://doi.org/10.1216/RMJ-2014-44-4-1111
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