Normal intermediate subfactors

摘要

The index theory for type Ⅱ_1 factors was initiated by V. Jones and the classification of subfactors has been studied by many people (etc.). A. Ocneanu introduced the concept of a paragroup to classify subfactors. By using the so-called standard invariants equivalent to the paragroups, S. Popa classified subfactors under more general conditions. The paragroups or the standard invariants for an inclusion of type Ⅱ_1 factors with finite Jones index is a group like object which generalizes finite groups. So the theory of finite groups may be considered as part of the index theory for an inclusion of type Ⅱ_1 factors with finite Jones index.