Das nicht-kommutative Michael-Auswahlprinzip und die Klassifikation nicht-einfacher Algebren

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C ∗ -algebras over topological spaces: the bootstrap class (2007, background): “Our definition is quite natural, but more restrictive than the definitions in [10, 4].”
Continuous fields of C*-algebras over finite dimensional spaces (2006, background): “A remarkable isomorphism result for separable nuclear strongly purely infinite stable C*algebras was announced (with an outline of the proof) by Kirchberg in [20]: two such C*-algebras A and B with the same primitive spectrum X are isomorphic if and only if they are KKC(X)equivalent.”
Central Sequences in C*-Algebras and Strongly Purely Infinite Algebras (2006, background): “(vi) If, in addition, u∗ ⊗ u ∈ U0(D ⊗ D) for every unitary u ∈ U(D) (equivalently: uvu∗v∗ ∈ U0(D) for all u, v ∈ U(D))), then the technics of [8] applies, and one can show that A ∼= A ⊗ D, if and only if, the quotient of A′ ∩ Cb(R+, A)/C0(R+, A) by the annihilator of A in Cb(R+, A)/C0(R+, A) contain”