Indecomposable characters of infinite dimensional groups associated with operator algebras

TL;DR

This paper characterizes the indecomposable characters of certain infinite dimensional groups linked to operator algebras, expanding understanding of their representation theory.

Contribution

It identifies the indecomposable characters for groups associated with unital simple AF algebras and II$_1$ factors, a novel classification in this context.

Findings

Characterization of indecomposable characters for these groups

Extension of representation theory to new classes of infinite dimensional groups

Provides a foundation for further analysis of operator algebra groups

Abstract

We determine the indecomposable characters of several classes of infinite dimensional groups associated with operator algebras, including the unitary groups of arbitrary unital simple AF algebras and II$_1$ factors.