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

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

1993-03-25

arxiv.org/abs/hep-th/9303142v1

Lett.Math.Phys.28:187-194,1993

Physics

High Energy Physics

High Energy Physics - Theory

8 pages

Scientific paper

10.1007/BF00745150

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 $B_1^\pm$, $B_2^\pm$.

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