SIMPLE C-ASTERISK-ALGEBRAS ARISING FROM BETA-EXPANSION OF REAL NUMBERS

Given a real number beta > 1, we construct a simple purely infinite C -algebra O-beta as a C-algebra arising from the beta-subshift in the symbolic dynamics. The C-argebras {O-beta}(1<beta is an element of R) interpolate between the Cuntz algebras {O-n}(1<n is an element of N). The K-groups for the C-algebras O-beta, 1 < beta is an element of R, are computed so that they are completely classified up to isomorphism . We prove that the KMS-state for the gauge action on O-beta is unique at the inverse temperature log beta, which is the topological entropy for the beta-shift. Moreover, O-beta is realized to be a universal C -algebra generated by n -1 = [beta] isometries and one partial isometr y with mutually orthogonal ranges and a certain relation coming from t he sequence of beta-expansion of 1.