CONJUGATE PAIRS OF SUBFACTORS AND ENTROPY FOR AUTOMORPHISMS

Abstract

Based on the fact that, for a subfactor N of a II1factor M, the first nontrivial Jones index is two and then M is decomposed as the crossed product of N by an outer action of ℤ2, we study pairs {N, uNu*} from the view-point of entropy for two subalgebras of M in connection with the entropy for automorphisms, where the inclusion of II1factors N ⊂ M is given with M being the crossed product of N by a finite group of outer automorphisms and u is a unitary in M.