Central Sequences in Subhomogeneous Unital C*-algebras

TL;DR

This paper characterizes when central sequences in unital subhomogeneous C*-algebras are hypercentral or trivial, based on the properties of limits of irreducible representations, providing new insights into their structure.

Contribution

It establishes precise conditions linking the nature of central sequences to limits of irreducible representations in subhomogeneous C*-algebras.

Findings

Central sequences are hypercentral iff limits of irreducible representations are multiplicity free.

Central sequences are trivial iff limits of irreducible representations are irreducible.

Provides a new representation for these algebras.

Abstract

Suppose A is a unital subhomogeneous C*-algebra. We show that every central sequence in A is hypercentral if and only if every pointwise limit of a sequence of irreducible representations is multiplicity free. We also show that every central sequence in A is trivial if and only if every pointwise limit of irreducible representations is irreducible. We also give a nice repesentation of the latter algebras.