Cuntz algebra

In mathematics, the Cuntz algebra ${\displaystyle {\mathcal {O}}_{n}}$, named after Joachim Cuntz, is the universal C*-algebra generated by n isometries satisfying certain relations. It is the first concrete example of a separable infinite simple C*-algebra.

Every simple infinite C*-algebra contains, for any given n, a subalgebra that has ${\displaystyle {\mathcal {O}}_{n}}$ as quotient.

Let n ≥ 2 and H be a separable Hilbert space. Consider the C*-algebra ${\displaystyle {\mathcal {A}}}$ generated by a set

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