Rotation Algebras and the Exel Trace Formula

Abstract

AbstractWe show that ifuandvare any two unitaries in a unitalC*–algebra such that ∥uv−vu∥ < 2 anduvu*v* commutes withuandv, then theC*–subalgebraAu,vgenerated by u and v is isomorphic to a quotient of some rotation algebraAθ, provided thatAu;vhas a unique tracial state. We also show that the Exel trace formula holds in any unitalC*–algebra. Let θ ∊ (−1/2, 1/2) be a real number. For any ∊ > 0; we prove that there exists ζ > 0 satisfying the following: if u and v are two unitaries in any unital simpleC*–algebra A with tracial rank zero such thatfor all tracial states τof A; then there exists a pair of unitariesandin A such that