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arXiv · 2212.08732

k1-injectivity of the Paschke dual algebra for certain simple C*-algebras

Jireh Loreaux·P. W. Ng·Arindam Sutradhar
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Abstract

Let $\mathcal{B}$ be a nonunital separable simple stable C*-algebra with strict comparison of positive elements and $T(\mathcal{B})$ having finite extreme boundary, and let $\mathcal{A}$ be a simple unital separable nuclear C*-algebra. We prove that the Paschke dual algebra $\mathcal{A}^d_{\mathcal{B}}$ is $K_1$-injective. As a consequence, we obtain interesting $KK$-uniqueness theorems which generalize the Brown-Douglas-Fillmore essential codimension property.

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Jireh Loreaux, P. W. Ng, Arindam Sutradhar. 2022-12-16. k1-injectivity of the Paschke dual algebra for certain simple C*-algebras. https://arxiv.org/abs/2212.08732

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