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

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

8 pages

Cited by in corpus (7)

• The quantum superalgebra $U_q[osp(1/2n)]$: deformed para-Bose operators and root of unity representations
• Hopf Structure and Green Ansatz of Deformed Parastatistics Algebras
• A Superalgebra Morphism of Uq[OSP(1/2N)] onto the Deformed Oscillator Superalgebra Wq(N)
• Algebraic structure of the Green's ansatz and its q-deformed analogue
• Unitarizable Representations of the Deformed Para-Bose Superalgebra Uq[osp(1/2)] at Roots of 1
• New Solutions of the Yang-Baxter Equation Based on Root of 1 Representations of the Para-Bose Superalgebra U${}_q$[osp(1/2)]
• Quantisation of U${}_q$[OSP(1/2N)] with Deformed Para-Bose Operators