Discrete product systems of finite-dimensional Hilbert spaces, and generalized Cuntz algebras
Operator Algebras
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/9904116,
title = {Discrete product systems of finite-dimensional Hilbert spaces, and generalized Cuntz algebras},
author = {Neal J. Fowler},
journal= {arXiv preprint arXiv:math/9904116},
year = {2007}
}
Comments
16 pages, AMS-LaTeX