Discrete product systems of finite-dimensional Hilbert spaces, and generalized Cuntz algebras

Neal J. Fowler

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arXiv · math/9904116

Discrete product systems of finite-dimensional Hilbert spaces, and generalized Cuntz algebras

Neal J. Fowler

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Abstract

To each discrete product system E of finite-dimensional Hilbert spaces we associate a C*-algebra O_E. When E is the n-dimensional product system over N, O_E is the Cuntz algebra O_n, and the irrational rotation algebras appear as O_E for certain one-dimensional product systems over N^2. We give conditions which ensure that O_E 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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Neal J. Fowler. 1999-04-21. Discrete product systems of finite-dimensional Hilbert spaces, and generalized Cuntz algebras. https://arxiv.org/abs/math/9904116

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