Nuclear dimension and n-comparison

Details Nuclear dimension and n-comparison Nuclear dimension and n-comparison

2010-02-10

arxiv.org/abs/1002.2180v2

Mathematics

Operator Algebras

changed introduction, added lemma

Scientific paper

It is shown that if a C*-algebra has nuclear dimension $n$ then its Cuntz
semigroup has the property of $n$-comparison. It then follows from results by
Ortega, Perera, and Rordam that $\sigma$-unital C*-algebras of finite nuclear
dimension (and even of nuclear dimension at most $\omega$) are stable if and
only if they have no non-zero unital quotients and no non-zero bounded traces.

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