Cuntz algebra

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A Cuntz algebra is a separable, simple purely infinite C*-algebra. In particular, take n ≥ 2, with n possibly infinite. Then the Cuntz algebra \mathcal{O}_n is defined to be the C*-algebra generated by a set

\{ S_i \}_{i=1}^{n}

of isometries of a separable Hilbert space satisfying

\sum_{i=1}^n S_i S_i^* = I or \forall k, \sum_{i=1}^k S_i S_i^* \leq I

respectively, if n is finite or infinite.

Note that, in particular, the Si have the property that

S_i^* S_j = \delta_{i,j} I

[edit] References

  • J. Cuntz, "Simple C*-Algebras Generated by Isometries," Comm. Math. Phys. 57, 173-185 (1977).


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