The C*-algebra of a Single Invertible Element

TL;DR

This paper characterizes the C*-algebra generated by a single invertible element as a free product of C[0,1] and C(T), using advanced techniques involving free products and Tietze transformations.

Contribution

It introduces a novel approach to describe the C*-algebra of an invertible element via free products and Tietze transformations, expanding the understanding of algebraic structures generated by single elements.

Findings

The C*-algebra generated by an invertible element is isomorphic to a free product of C[0,1] and C(T).

Develops techniques to manipulate presentations of C*-algebras using free products and Tietze transformations.

Provides a new framework for analyzing the structure of C*-algebras generated by single elements.

Abstract

This paper characterizes the unital C*-algebra generated by a single invertible element as the unital free product of C[0,1] and C(T). To do this, I develop techniques to split and merge presentations of C*-algebras using free products in tandem with the Tietze transformations devised in my previous paper.