On a possible algebra morphism of U$_q$[OSP(1/2N)] onto the deformed oscillator algebra W$_q$(N)

TL;DR

This paper explores the algebraic relationship between the quantum superalgebra U_q[osp(1/2n)] and deformed oscillator algebras, providing a proof for the case n=2 and conjecturing a general factor-algebra structure.

Contribution

It formulates and proves a conjecture that U_q[osp(1/2n)] is a factor-algebra of deformed oscillator algebras for n=2, extending understanding of their algebraic connections.

Findings

U_q[osp(1/4)] can be viewed as generated by deformed para-Bose operators

All Hopf algebra relations and basis can be expressed in terms of these operators

The conjecture is proven explicitly for the case n=2

Abstract

We formulate a conjecture, stating that the algebra of $n$ pairs of deformed Bose creation and annihilation operators is a factor-algebra of $U_q[osp(1/2n)]$, considered as a Hopf algebra, and prove it for $n=2$ case. To this end we show that for any value of $q$ $U_q[osp(1/4)]$ can be viewed as a superalgebra, freely generated by two pairs $B_1^\pm$, $B_2^\pm$ of deformed para-Bose operators. We write down all Hopf algebra relations, an analogue of the Cartan-Weyl basis, the "commutation" relations between the generators and a basis in $U_q[osp(1/2n)]$ entirely in terms of $B_1^\pm$, $B_2^\pm$.