Faithfulness of the Fock representation of $C^{\ast }$-algebra generated by $q_{ij}$-commuting isometries

Abstract

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

16 pages

References in corpus (1)

• On C*-algebras generated by pairs of q-commuting isometries