The C*-algebra of the Boidol group

TL;DR

This paper characterizes the C*-algebra of the Boidol group, a unique 4-dimensional non-*-regular exponential Lie group, by describing it as an algebra of operator fields over its spectrum.

Contribution

It provides the first detailed description of the C*-algebra for the Boidol group, expanding understanding of solvable Lie group C*-algebras.

Findings

C*-algebra described as operator fields over the spectrum

Boidol group is the smallest non-*-regular exponential Lie group with known C*-algebra

Unique determination among low-dimensional solvable Lie groups

Abstract

The Boidol group is the smallest non-*-regular exponential Lie group. It is of dimension 4 and its Lie algebra is an extension of the Heisenberg Lie algebra by the reals with the roots 1 and -1. We describe the C*-algebra of the Boidol group as an algebra of operator fields defined over the spectrum of the group. It is the only connected solvable Lie group of dimension less than or equal to 4 whose group C*-algebra had not yet been determined.