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

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 $μ\in[0,4]$. These $μ$-constrained representations determine a C*-algebra $A_μ$ for each $μ\in[0,4]$. We prove that these C*-algebras form a continuous bundle of C*-algebras over $[0,4]$ and calculate their K-groups.

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