A classification of all finite index subfactors for a class of group-measure space II_1 factors

TL;DR

This paper classifies all finite index subfactors of certain group-measure space II_1 factors, explicitly listing them and computing their indices, with examples showing the index set can be any divisor-closed natural numbers.

Contribution

It provides a complete classification of finite index subfactors for a specific class of II_1 factors, including explicit index set computations.

Findings

All finite index subfactors can be explicitly listed.

The set of all indices of irreducible subfactors can be any divisor-closed natural numbers.

Concrete examples demonstrate the possible index sets.

Abstract

We provide a family of group measure space II_1 factors for which all finite index subfactors can be explicitly listed. In particular, the set of all indices of irreducible subfactors can be computed. Concrete examples show that this index set can be any set of natural numbers that is closed under taking divisors.