Discrete product systems of finite-dimensional Hilbert spaces, and generalized Cuntz algebras
Abstract
To each discrete product system E of finite-dimensional Hilbert spaces we associate a C*-algebra OE. When E is the n-dimensional product system over N, OE is the Cuntz algebra On, and the irrational rotation algebras appear as OE for certain one-dimensional product systems over N2. We give conditions which ensure that OE is simple, purely infinite, and nuclear. Our main examples are the lexicographic product systems, for which we obtain slightly stronger results.
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