Quantization of the Lie Algebra SO(2N+1) and of the Lie Superalgebra Osp(1/2N) with Preoscillator Generators

TL;DR

This paper presents a quantization method for the Lie algebra so(2N+1) and the Lie superalgebra osp(1/2N) using preoscillator generators, connecting them to deformed para-Fermi and para-Bose operators.

Contribution

It introduces a unified quantization framework for these algebras with preoscillator generators, linking them to deformed universal enveloping algebras and known deformed operators.

Findings

Preoscillator generators reduce to deformed Fermi and Bose operators in certain representations.

The quantized algebras match the Chevalley operator-based definitions.

Unified approach applies to both Lie algebra and superalgebra cases.

Abstract

The Lie algebra $so(2n+1)$ and the Lie superalgebra $osp(1/2n)$ are quantized in terms of $3n$ generators, called preoscillator generators. Apart from $n$ "Cartan" elements the preoscillator generators are deformed para-Fermi operators in the case of $so(2n+1)$ and deformed para-Bose operators in the case of $osp(1/2n)$. The corresponding deformed universal enveloping algebras $U_q[so(2n+1)]$ and $U_q[osp(1/2n)]$ are the same as those defined in terms of Chevalley operators. The name "preoscillator" is to indicate that in a certain representation these operators reduce to the known deformed Fermi and Bose operators.