K-theory for the simple C∗-algebra of the Fibonacci-Dyck shift

The Fibonacci-Dyck shift DF is a subsystem of the Dyck shift D2 constrained by the Fibonacci matrix F = [1110]. Let £Ch(Df) be a certain λ-graph system presenting the subshift DF, which is a labeled Bratteli diagram with some additional structure. The C∗-algebra O£ Ch(Df) associated with £Ch(Df) is simple purely infinite and generated by four partial isometries with some operator relations. We will compute the K-theory of the C∗-algebra. As a result, the C∗-algebra is not stably isomorphic to any Cuntz-Krieger algebra nor to the C∗-algebras O£ Ch(DN) OF the Dyck shifts DN. We will also know that the subshift DF is not flow equivalent to any of Dyck shifts DN, 1 < N ϵ ℕ. © Bolyai Institute, University of Szeged.