Conjugate Pairs of Subfactors and Entropy for Automorphisms

TL;DR

This paper explores the relationship between conjugate pairs of subfactors in II$_1$ factors and entropy, focusing on automorphisms arising from crossed product constructions with finite groups.

Contribution

It introduces a novel perspective linking subfactor pairs and entropy for automorphisms, especially in the context of crossed products by finite groups.

Findings

Characterization of conjugate subfactor pairs via entropy measures

Connection between Jones index 2 and automorphism entropy

Analysis of entropy behavior under crossed product constructions

Abstract

Based on the fact that, for a subfactor $N$ of a II$_1$ factor $M,$ the first non-trivial Jones index is 2 and then $M$ is decomposed as the crossed product of $N$ by an outer action of ${\mathbb{Z}}_2,$ we study pairs $ \{N, uNu^* \}$ from a view point of entropy for two subalgebras of $M$ with a connection to the entropy for automorphisms, where the inclusion of II$_1$ factors $ N \subset M$ is given as $M$ is the crossed product of $N$ by a finite group of outer automorphisms and $u$ is a unitary in $M.$