AF flows and continuous symmetries
  We consider AF-flows, i.e., one-parameter automorphism groups of a unital simple C*-algebra which leave invariant the dense union of an increasing sequence of finite-dimensional *-subalgebras, and derive two properties for these; an absence of continuous symmetry breaking and a kind of real rank zero property for the almost fixed points. 
Ola Bratteli and Akitaka Kishimoto