K-THEORETIC INVARIANTS AND CONFORMAL MEASURES OF THE DYCK SHIFTS

Abstract

The K-groups and the Bowen–Franks groups for subshifts are invariant under not only topological conjugacy but also flow equivalence. In this paper, the K-groups and the Bowen–Franks groups for the Dyck shift D2 with 4 brackets are calculated. The spectrum of D2 with bounded nonnegative eigenvectors is shown to be the singleton {3}. We then prove that a unique conformal probability measure on the right one-sided subshift XD2 exists. These results are extended to general Dyck shifts DN with 2N brackets.