Let A be a unital AH-algebra and let α ∈ Aut(A) be an automorphism. A necessary condition for A ⋊α Z being embedded into a unital simple AF-algebra is the existence of a faithful tracial state. If in addition, there is an automorphism κ with κ∗1 = −idK1(A) such that α ◦ κ and κ ◦ α are asymptotically unitarily equivalent, then A⋊α Z can be embedded into a unital simple AF-algebra. Consequently,...

We study topological properties of conjugacy classes in Polish groups, with emphasis on automorphism groups of homogeneous countable structures. We first consider the existence of dense conjugacy classes (the topological Rokhlin property). We then characterize when an automorphism group admits a comeager conjugacy class (answering a question of Truss) and apply this to show that the homeomorphi...

We initiate a study of linear maps on Mn(C) that have the property they factor through tracial von Neumann algebra (A,τ) via operators Z∈Mn(A) whose entries consist positive elements from von-Neumann algebra. These often arise in context non-local games especially synchronous case. establish connection with convex sets Rn containing self-dual cones and existence these maps. The Choi matrix map ...

Let C be a unital AH-algebra and let A be a unital separable simple C∗-algebra with tracial rank zero. Suppose that φ1, φ2 : C → A are two unital monomorphisms. We show that there is a continuous path of unitaries {ut : t ∈ [0,∞)} of A such that lim t→∞ u∗tφ1(a)ut = φ2(a) for all a ∈ C if and only if [φ1] = [φ2] in KK(C,A), τ ◦ φ1 = τ ◦ φ2 for all τ ∈ T (A) and the rotation map η̃φ1,φ2 associate...

Using various finite dimensional approximation properties, four convex subsets of the tracial space of a unital C∗-algebra are defined. One subset is characterized by Connes’ hypertrace condition. Another is characterized by hyperfiniteness of GNS representations. The other two sets are more mysterious but are shown to be intimately related to Elliott’s classification program. Applications of t...

Abstract Let $$\phi $$ ϕ be a positive map from the $$n\times n$$ n × matrices $$\mathcal {M}_n$$ M to $$m\times m$$ m {M}_m$$ . It is known that 2-positive if and only for all $$K\in \mathcal <mm...

Abstract We construct two types of unital separable simple $C^*$ -algebras: $A_z^{C_1}$ and $A_z^{C_2}$ , one exact but not amenable, the other nonexact. Both have same Elliott invariant as Jiang–Su algebra – namely, $A_z^{C_i}$ has a unique tracial state, $$ \begin{align*} \left(K_0\left(A_z^{C_i}\right), K_0\left(A_z^{C_i}\right)_+, \left[1_{A_z^{C_i}} \right]\right)=(\mathbb{Z}, \mathbb{Z}_+...