Dimension growth for C*-algebras

• Autores: Andrew S. Toms
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 213, Nº 2, 2007, págs. 820-848
• Idioma: inglés
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• Resumen

  • We introduce the growth rank of a C*-algebra-a -valued invariant whose minimal instance is equivalent to the condition that an algebra absorbs the Jiang-Su algebra tensorially-and prove that its range is exhausted by simple, nuclear C*-algebras. As consequences we obtain a well developed theory of dimension growth for approximately homogeneous (AH) C*-algebras, establish the existence of simple, nuclear, and non- -stable C*-algebras which are not tensorially prime, and show the assumption of -stability to be particularly natural when seeking classification results for nuclear C*-algebras via K-theory. The properties of the growth rank lead us to propose a universal property which can be considered inside any class of unital and nuclear C*-algebras. We prove that satisfies this universal property inside a large class of locally subhomogeneous algebras, representing the first uniqueness theorem for which does not depend on the classification theory of nuclear C*-algebras.