Galois quantum groups of II_1-subfactors

Abstract

We give a correspondence between a class of quantum groups (face algebras) and a class of AFD II_1-subfactors, which contains both all of those of index less than 4 and all of those of principal graph D_n⁽¹⁾ or E_n⁽¹⁾. Ocneanu's flat connection and a variant of Woronowicz's compact quantum group theory play central roles.