2005/09/07 by Andrew S. Toms, Toms, Andrew S. · 1 citation
Mathematics · #46L35 #46L80 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.math/0509159
openalex publication_date 2005/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the growth rank of a C*-algebra, a (N ∪ ∞)-valued invariant which measures how far an algebra is from absorbing the Jiang-Su algebra Z tensorially. We prove that its range is exhausted by simple nuclear C*-algebras, and obtain in the process a well developed theory of unbounded dimension growth for approximately homogeneous (AH) algebras. Another consequence of the range result is the existence of a simple, nuclear, and non-Z-stable C*-algebra which is not tensorially prime. The properties of the growth rank suggest a universal property which may be considered inside any class of unital and nuclear C*-algebras. We prove that Z satisfies this property inside a class of locally subhomogeneous algebras.