K₁-injectivity of the Paschke dual algebra, and uniqueness

2021/06/25 by Loreaux, Jireh, Ng, P. W., Sutradhar, Arindam
#FOS: Mathematics #K-Theory and Homology (math.KT) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2106.13370

Abstract

We prove that a large class of Paschke dual algebras of simple unital C*-algebras are K₁-injective. As a consequence, we obtain interesting KK-uniqueness theorems which generalize the Brown--Douglas--Fillmore essential codimension property.

Related

• k1-injectivity of the Paschke dual algebra for certain simple C*-algebras
• A properly infinite C*-algebra which is not K₁-injective
• Amenability and Uniqueness
• K₁-injectivity for properly infinite C*-algebras
• Injective envelopes for locally C*-algebras