Quasidiagonal extensions and AF algebras.

• Authors:Søren Eilers, Terry A. Loring and Gert K. Pedersen.
• Date: November 1996.
• Status: Appeared in Mathematische Annalen, 311 (1998), 233-249.
• Pages: 16.
• Abstract: Suppose that X is a separable C*-algebra with a closed ideal A such that X/A is approximately finite-dimensional. Given a quasidiagonal extension 0 ---> k ---> E ---> A ---> 0 we can find E' to complete the commutative diagram 0 ---> k ---> E ---> A ---> 0
  
  
  0 ---> k ---> E' ---> X ---> 0
  so that the bottom row is also a quasidiagonal extension. As a corollary we find that X is nuclear and quasidiagonal if and only if A is nuclear and quasidiagonal.
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