Compact Group Actions On Operator Algebras and Their Spectra

TL;DR

This paper investigates the relationship between algebraic properties of fixed point algebras and spectral properties of dynamical systems involving compact non-abelian groups, encompassing C*-, W*-, and multiplier systems.

Contribution

It establishes new connections between algebraic simplicity or primeness and spectral characteristics like Connes spectra in such dynamical systems.

Findings

Fixed point algebra properties relate to spectral features.

Results apply to C*-, W*-, and multiplier dynamical systems.

Provides criteria linking algebraic and spectral properties.

Abstract

We consider a class of dynamical systems with compact non abelian groups that include C*-, W*- and multiplier dynamical systems. We prove results that relate the algebraic properties such as simplicity or primeness of the fixed point algebras as defned in Section 3., to the spectral properties of the action, including the Connes and strong Connes spectra.