The C*-algebras of connected real two-step nilpotent Lie groups

TL;DR

This paper characterizes the C*-algebras of connected real two-step nilpotent Lie groups using operator valued Fourier transforms, showing they satisfy the norm controlled dual limit property through explicit computations.

Contribution

It provides a detailed description of these C*-algebras as operator field algebras and verifies the norm controlled dual limit property explicitly.

Findings

C*-algebras are characterized as operator fields over spectra

Fourier transform satisfies the norm controlled dual limit property

Explicit computations support the theoretical framework

Abstract

Using the operator valued Fourier transform, the C*-algebras of connected real two-step nilpotent Lie groups are characterized as algebras of operator fields defined over their spectra. In particular, it is shown by explicit computations, that the Fourier transform of such C*-algebras fulfills the norm controlled dual limit property.