C0 (X)-algebras, stability and strongly self-absorbing C∗-algebras Academic Article uri icon

abstract

  • Abstract We study permanence properties of the classes of stable and so-called D-stable C∗- algebras, respectively. More precisely, we show that a C0 (X)-algebra A is stable if all its fibres are, provided that the underlying compact metrizable space X has finite covering dimension or that the Cuntz semigroup of A is almost unperforated (a condition which is automatically satisfied for C∗-algebras absorbing the Jiang–Su algebra Z tensorially). Furthermore, we prove that if D is a K1-injective strongly self-absorbing C∗-algebra, then …

publication date

  • March 8, 2007