### Nuclear dimension and n-comparisonNuclear dimension and n-comparison

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 Author Robert, Leonel Source arXiv.org Content type Text File Format PDF Date of Submission 2010-02-10 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Operator Algebras ♦ math Abstract 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. Educational Use Research Learning Resource Type Article