Maximal subalgebras of C*-algebras associated with periodic flows

TL;DR

This paper characterizes when the subalgebra of analytic elements in a periodic C*-dynamical system is maximal, using spectra and simplicity conditions, advancing understanding of subalgebra structures in operator algebras.

Contribution

It provides necessary and sufficient spectral conditions for maximality of analytic subalgebras in periodic C*-dynamical systems.

Findings

Conditions in terms of Arveson spectrum for maximality

Characterization using strong Connes spectrum

Relation to simplicity of crossed product

Abstract

We find necessary and sufficient conditions for the subalgebra of analytic elements associated with a periodic C*-dynamical system to be a maximal norm-closed subalgebra. Our conditions are in terms of the Arveson spectrum of the action. We also describe equivalent properties of the system in terms of the strong Connes spectrum and the simplicity of the crossed product.