Is it possible to extend the deformed Weyl algebra $W_q(n)$ to a Hopf algebra?

Abstract

We argue that the algebra $W_q(n)$, generated by $n$ pairs of deformed $q$-bosons, does not allow a Hopfalgebra structure. To this end we show that it is impossible to define a comultiplication even for the usual, nondeformed case. We indicate how the comultiplication on $U_q[osp(1/2n)]$ can be used in order to construct representations of deformed (not necessarily Hopf) algebras in tensor products of Fock spaces.