# Journal of Operator Theory

Volume 78, Issue 2, Fall 2017 pp. 435-472.

On the $\mathrm{KK}$-theory of Elliott-Thomsen algebras

**Authors**:
Qingnan An (1) and George A. Elliott (2)

**Author institution:**(1) Department of Mathematics, Jilin University,
Changchun, 130012, P. R. China

(2) Department of Mathematics, University of
Toronto, Toronto, Ontario, Canada M5S 2E4

**Summary: **This paper concerns the $\mathrm{KK}$-theory of the class
$\mathcal{C}$ of
Elliott-Thomsen algebras,
with special emphasis on the problem of when a $\mathrm{KK}$-element can be represented by a homomorphism between two such $C^*$-alge\-bras (allowing the tensor product with a matrix algebra for the codomain algebra), and gives an existence theorem for a certain subclass of
$\mathcal{C}$ which we
denote by $\mathcal{C}_\mathcal{O}$.

**DOI: **http://dx.doi.org/10.7900/jot.2016oct03.2155

**Keywords: **Elliott-Thomsen algebra, $\mathrm{KK}$-theory, $\mathrm{KK}$-lifting, $\mathrm{mod}$-$p$ $\mathrm{K}$-theory

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