On the inductive limit structure of order four automorphisms of the irrational rotation algebra

摘要

It is shown that there exists an order four automorphism of the irrational rotation algebra A(theta) that leaves invariant an increasing sequence of unital C*-subalgebras consisting of two circles and two points and such that its induced map on K-1(A(theta)) is given by the The resulting fixed point algebra is shown to be approximately finite-matrix dimensional. A brief survey of recent work on the canonical finite order automorphisms of A(theta) is given and some open problems are posed.