INVARIANTS OF STATIONARY AF-ALGEBRAS AND TORSION SUBGROUPS OF ELLIPTIC CURVES WITH COMPLEX MULTIPLICATION

Let G(A) be an AF-algebra given by a periodic Bratteli diagram with the incidence matrix A is an element of GL(n,Z). For a given polynomial p(x) is an element of Z[x] we assign to G(A) a finite abelian group Ab(p(x))(G(A)) = Z(n)/p(A)Z(n). It is shown that if p(0) = 1 and Z[x]/< p(x) is a principal ideal domain, then Ab(p(x))(G(A)) is an invariant of the strong stable isomorphism class of G(A). For n = 2 and p(x) = x - 1 we conjecture a formula linking values of the invariant and torsion subgroup of elliptic curves with complex multiplication.