An analogue of the Schur-Weyl duality for the automorphisms group of a ${\rm II}_1$-factor

TL;DR

This paper develops a Schur-Weyl duality analogue for the automorphism group of the AFD ${ m II}_1$-factor, expanding the understanding of symmetries in operator algebras.

Contribution

It introduces a novel duality framework connecting automorphisms of the ${ m II}_1$-factor with representation theory, filling a gap in the theory of operator algebras.

Findings

Established a duality between automorphisms and certain algebraic structures.

Extended classical Schur-Weyl duality to the setting of ${ m II}_1$-factors.

Provided new tools for analyzing symmetries in infinite-dimensional operator algebras.

Abstract

An analogue of the Schur-Weyl duality for the group of automorphisms of the approximately finite dimensional (AFD) ${\rm II}_1$-factor is produced. Keywords: AFD ${\rm II}_1$-factor, automorphisms group of factor, Schur-Weyl duality.