On locally finite-dimensional traces II

We continue the study of locally finite-dimensional traces introduced in our earlier work. We give new characterizations of LFD traces in terms of finite-rank projections in irreducible representations and in the socle of the bidual. We show that, for separable nowhere scattered $C^{\ast }$-algebras, the set of all LFD traces is convex. We also prove that quasidiagonal traces form a face of the trace simplex and record applications to strongly self-absorbing $C^{\ast }$-algebras. We construct an exact tracially AF algebra not KK-equivalent to any nuclear $C^{\ast }$-algebra.