On $C^*$-algebra generated by Fock representation of Wick algebra with braided coefficients

Abstract

We consider $C^*$-algebras $\mathcal{W}(T)$ generated by operators of Fock representations of Wick $*$-algebras with a braided coefficient operator $T$. It is shown that for any braided $T$ with $||T||<1$ one has the inclusion $\mathcal{W}(0)\subset\mathcal{W}(T)$. Conditions for existence of an isomorphism $\mathcal{W}(T)\simeq\mathcal{W}(0)$ are discussed.