Elementary approach to homogeneous C*-algebras

TL;DR

This paper provides an elementary proof of Fell's characterization of finite-dimensional homogeneous C*-algebras, along with a spectral theorem and functional calculus for their generators.

Contribution

It introduces a simplified proof of Fell's theorem and develops spectral tools for n-homogeneous C*-algebras, enhancing understanding and analysis methods.

Findings

Elementary proof of Fell's characterization

Spectral theorem for n-homogeneous C*-algebras

Functional calculus for generators

Abstract

A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their spectra) is presented. A spectral theorem and a functional calculus for finite systems of elements which generate n-homogeneous C*-algebras are proposed.