Extensions of the UHF-algebra of 2∞-type by C*-algebras with continuous scale

Let A be the UHF-algebra of 2(infinity)-type, B be a non-unital but sigma-unital stably finite simple C*-algebra with real rank zero and a continuous scale. In this paper, we give a classification of the following essential extensions of A by B circle times A: 0 -> B circle times A -> E -> A -> 0, up to unitary equivalence. Denote by Ext(A, B circle times A), the abelian group of unitary equivalence classes of essential extensions of A by B circle times A. There is a group isomorphism Gamma : Ext(A, B circle times A) -> KK (A, rho(B circle times A)) defined by Gamma([tau]) := [tau] KK, where rho (B circle times A) is the corona algebra of B circle times A. (C) 2021 Elsevier Inc. All rights reserved.