Dimension growth for $C^*$-algebras
| dc.creator | Toms, Andrew S. | |
| dc.date | 2005-09-07 | |
| dc.date | 2007-01-31 | |
| dc.date.accessioned | 2026-07-07T07:43:51Z | |
| dc.date.available | 2026-07-07T07:43:51Z | |
| dc.description | We introduce the growth rank of a C*-algebra, a (N \cup {\infty})-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. | |
| dc.description | 26 pages; minor revisions; to appear in Adv. Math | |
| dc.identifier | https://arxiv.org/abs/math/0509159 | |
| dc.identifier | http://arxiv.org/abs/math/0509159 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122987 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L35; 46L80 | |
| dc.title | Dimension growth for $C^*$-algebras | |
| dc.type | text |