Consider the Cuntz algebra $O_2$. Is it true that $M_2(O_2)$ is isomorphic to $O_2$? I was trying to show that is impossible but now I am not sure.
2026-04-03 21:41:52.1775252512
Matrices over the Cuntz algebra
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Yes, it is true. In fact, if $A$ is a simple, separable, unital, nuclear $C^{\ast}$-algebra, then $A\otimes O_2 \cong O_2$. This is a theorem of Kirchberg [See Theorem 7.1.2 in Rordam's book]