The Ext-group of unitary equivalence classes of unital extensions

Abstract

Let A be a unital separable nuclear C * -algebra which belongs to the bootstrap category N and B be a separable stable C * -algebra. In this paper, we consider the group Extu(A, B) consisting of the unitary equivalence classes of unital extensions τ : A → Q(B). The relation between Extu(A, B) and Ext(A, B) is established. Using this relation, we show the half-exactness of Extu(·, B) and the (UCT) for Extu(A, B). Furthermore, under certain conditions, we obtain the half-exactness and Bott periodicity of Extu(A, ·).

Topologizing UCTs for unital extensions

“…where A is a unital C*-algebra in the class N . Under the circumstance of unital extensions, a UCT for the stable strong Ext-group in a general form was established in [20,21] (also see [23,27,33]) 1 :…”