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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 $\mathcal{C}_\mathcal{O}$.

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

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