Let A be a unital simple AT-algebra of real rank zero. Given an isomorphism γ1 : K1(A)→ K1(A), we show that there is an automorphism α : A → A such that α∗1 = γ1 which has the tracial Rokhlin property. Consequently, the crossed product A ⋊α Z is a simple unital AH-algebra with real rank zero. We also show that automorphism with Rokhlin property can be constructed from minimal homeomorphisms on ...

Let A be a simple unital C∗-algebra with tracial rank zero and with a unique tracial state and let Φ be an involutory ∗-antiautomorphism of A. It is shown that the associated real algebra AΦ = {a ∈ A : Φ(a) = a∗} also has tracial rank zero. Let A be a unital simple separable C∗-algebra with tracial rank zero and suppose that A has a unique tracial state. If Φ is an involutory ∗-antiautomorphism...

1 The minimum rank problem for a (simple) graph G is to determine the smallest possible 2 rank over all real symmetric matrices whose ijth entry (for i 6= j) is nonzero whenever {i, j} 3 is an edge in G and is zero otherwise. This paper surveys the many developments on the 4 (standard) minimum rank problem and its variants since the survey paper [36]. In particular, 5 positive semidefinite mini...

We prove the title, establishing the existence of a quasitrace on a (unital, simple) C-algebra (of real rank zero and stable rank one), which is not a tracial state.

Let A be a unital separable simple C∗-algebra with TR(A) ≤ 1 and α be an automorphism. We show that if α satisfies the tracially cyclic Rokhlin property then TR(A ⋊α Z) ≤ 1. We also show that whenever A has a unique tracial state and αm is uniformly outer for each m and αr is approximately inner for some r > 0, α satisfies the tracial cyclic Rokhlin property. By applying the classification theo...