A Superalgebra Morphism of Uq[OSP(1/2N)] onto the Deformed Oscillator Superalgebra Wq(N)

TL;DR

This paper demonstrates that the deformed oscillator superalgebra W_q(n) can be derived as a factor algebra from the quantized universal enveloping algebra U_q[osp(1/2n)], providing a new algebraic relationship.

Contribution

It establishes a superalgebra morphism linking U_q[osp(1/2n)] to W_q(n) and constructs a q-analog of the Cartan-Weyl basis with oscillator realizations.

Findings

W_q(n) is a factor algebra of U_q[osp(1/2n)]

Constructed a q-analog of the Cartan-Weyl basis

Provided an oscillator realization of Cartan-Weyl generators

Abstract

We prove that the deformed oscillator superalgebra $W_q(n)$ (which in the Fock representation is generated essentially by $n$ pairs of $q$-bosons) is a factor algebra of the quantized universal enveloping algebra $U_q[osp(1/2n)]$. We write down a $q$-analog of the Cartan-Weyl basis for the deformed $osp(1/2n)$ and give also an oscillator realization of all Cartan-Weyl generators.