A purely infinite AH-algebra and an application to AF-embeddability

Details A purely infinite AH-algebra and an application to AF-embeddability A purely infinite AH-algebra and an application to AF-embeddability

2002-05-28

arxiv.org/abs/math/0205292v2

Israel J. Math. 141 (2004), 61-82

Mathematics

Operator Algebras

20 pages, revised January 2004, to appear in Israel J. Math

Scientific paper

We show that there exists a purely infinite AH-algebra. The AH-algebra arises as an inductive limit of C*-algebras of the form C_0([0,1),M_k) and it absorbs the Cuntz algebra O_\infty tensorially. Thus one can reach an O_\infty-absorbing C*-algebra as an inductive limit of the finite and elementary C*-algebras C_0([0,1),M_k). As an application we give a new proof of a recent theorem of Ozawa that the cone over any separable exact C*-algebra is AF-embeddable, and we exhibit a concrete AF-algebra into which this class of C*-algebras can be embedded.

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