Resumen de Dimension growth for C*-algebras

Andrew S. Toms

• 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.