Purely infinite C*-algebras: ideal-preserving zero homotopies

Details Purely infinite C*-algebras: ideal-preserving zero homotopies Purely infinite C*-algebras: ideal-preserving zero homotopies

2003-12-15

arxiv.org/abs/math/0312286v1

Geom. Funct. Anal., 15, No. 2, (2005), 377-415

Mathematics

Operator Algebras

42 pages

Scientific paper

We show that if A is a separable, nuclear, O_infty-absorbing (or strongly purely infinite) C*-algebra, which is homotopic to zero in an ideal-system preserving way, then A is the inductive limit of C*-algebras of the form M_k(C_0(G,v)), where G is a finite graph (and C_0(G,v) is the algebra of continuous functions on G that vanish at a distinguished point v in G). We show further that any separable, nuclear, stable, O_2-absorbing C*-algebra is isomorphic to a crossed product of a C*-algebra D with the integers by an action alpha, where D is an inductive limit of C*-algebras of the form M_k(C_0(G,v)) (and D is O_2-absorbing and homotopic to zero in an ideal-system preserving way).

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