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Faithfulness of the Fock representation of $C^*$-algebra generated by $q_{ij}$-commuting isometries by Kuzmin, Alexey; Pochekai, Nikolay is a scholarly article available to read on EtoBox.

What is Faithfulness of the Fock representation of $C^*$-algebra generated by $q_{ij}$-commuting isometries about?

We consider $C^*$-algebra $Isom_{q_{ij}}$ generated by $n$ isometries $a_1, \ldots, a_n$ satisfying the relations $a_i^* a_j = q_{ij} a_j a_i^*$ with $\max |q_{ij}| < 1$. This $C^*$-algebra is shown to be nuclear. We prove that the Fock representation of $Isom_{q_{ij}}$ is faithful. Further we describe an ideal in $Isom_{q_{ij}}$ which is isomorphic to the algebra of compact operators.

Author

Kuzmin, Alexey; Pochekai, Nikolay

Published

2017

Language

EN