On C*-algebras related to constrained representations of a free group

TL;DR

This paper studies a family of C*-algebras arising from constrained representations of the free group on two generators, showing they form a continuous bundle over a parameter interval and computing their K-theory.

Contribution

It introduces a new class of C*-algebras defined by norm constraints on free group representations and analyzes their structural properties.

Findings

C*-algebras form a continuous bundle over [0,4]

K-groups of these algebras are explicitly calculated

The structure varies continuously with the parameter 

Abstract

We consider representations of the free group $F_2$ on two generators such that the norm of the sum of the generators and their inverses is bounded by $\mu\in[0,4]$. These $\mu$-constrained representations determine a C*-algebra $A_{\mu}$ for each $\mu\in[0,4]$. We prove that these C*-algebras form a continuous bundle of C*-algebras over $[0,4]$ and calculate their K-groups.