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

Tchavdar D. Palev

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arXiv · hep-th/9412060

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

Tchavdar D. Palev

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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.

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Tchavdar D. Palev. 1994-12-16. Quantization of the Lie Algebra SO(2N+1) and of the Lie Superalgebra Osp(1/2N) with Preoscillator Generators. https://arxiv.org/abs/hep-th/9412060

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