publication . Preprint . Other literature type . Article . 2002

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

Mikael Rørdam;
Open Access English
  • Published: 28 May 2002
  • Country: Philippines
Abstract
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.
Subjects
arXiv: Mathematics::Operator Algebras
free text keywords: Mathematics - Operator Algebras, 46L05, 46L35, 19K14, General Mathematics, Quaternion algebra, Cuntz algebra, Differential graded algebra, Mathematical analysis, Algebra representation, Current algebra, Symmetric algebra, Algebra, Cellular algebra, Filtered algebra, Mathematics
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publication . Preprint . Other literature type . Article . 2002

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

Mikael Rørdam;