K_1$-injectivity of the Paschke dual algebra, and uniqueness

K_1$-injectivity of the Paschke dual algebra, and uniqueness

We prove that a large class of Paschke dual algebras of simple unital C*-algebras are $K_1$-injective. As a consequence, we obtain interesting $KK$-uniqueness theorems which generalize the Brown--Douglas--Fillmore essential codimension property.

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Hauptverfasser: Loreaux, Jireh, Ng, P. W, Sutradhar, Arindam
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - K-Theory and Homology
Mathematics - Operator Algebras
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Zusammenfassung:We prove that a large class of Paschke dual algebras of simple unital C*-algebras are $K_1$-injective. As a consequence, we obtain interesting $KK$-uniqueness theorems which generalize the Brown--Douglas--Fillmore essential codimension property.
DOI:10.48550/arxiv.2106.13370