M$\ddot{o}$bius Disjointness for Exact C$^*$ Algebras

TL;DR

This paper extends the concept of M"obius disjointness to various classes of C$^*$-algebras, analyzing its properties and implications for algebraic structures with automorphisms.

Contribution

It introduces M"obius disjointness in the context of C$^*$-algebras and explores its application to several important algebra classes.

Findings

M"obius disjointness is established for finite dimensional C$^*$-algebras.

The concept is analyzed for finite von Neumann algebras.

Applications to free group and CAR algebras are discussed.

Abstract

In this paper we introduce the M\"obius disjointness for C$^*$-algebras with their automorphisms and studied the M\"obius disjointness for finite dimensional C$^*$ algebras, finite von Neumann algebras, reduced free group algebra and canonical anticommutation relation algebra etc.