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Cuntz Algebra


The Cuntz algebra O_n, for an integer n>=2, is the universal unital C*-algebra generated by s_1, ..., s_n with

 s_i^*s_j=delta_(ij)1,

and

 sum_(i=1)^ns_is_i^*=1.

Thus the generators are isometries with mutually orthogonal ranges summing to the identity. These algebras are simple and nuclear. In particular, O_2 is the target algebra in Kirchberg's embedding problem.


See also

C*-Algebra, Kirchberg's Embedding Problem, Nuclear C*-Algebra, Purely Infinite C-Star-Algebra

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References

Blackadar, B. Operator Algebras: Theory of C*-Algebras and von Neumann Algebras. Berlin, Germany: Springer, 2006. https://doi.org/10.1007/3-540-28517-2.

Cite this as:

Weisstein, Eric W. "Cuntz Algebra." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CuntzAlgebra.html

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