# Subfactors and Hecke groups

## TL;DR

This paper explores the connection between Hecke groups and subfactor indices in von Neumann algebras, addressing a problem posed by V. F. R. Jones, through the application of cluster C*-algebras.

## Contribution

It introduces a novel approach linking Hecke groups and subfactor indices using cluster C*-algebras, solving a longstanding problem.

## Key findings

- Established a relationship between Hecke groups and subfactor indices.
- Applied cluster C*-algebras to analyze subfactors.
- Provided new insights into the structure of von Neumann algebra subfactors.

## Abstract

We study a relation between the Hecke groups and the index of subfactors in a von Neumann algebra. Such a problem was raised by V. F. R. Jones. We solve the problem using the notion of a cluster C*-algebra.