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

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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 Uq[so(2n+1)] and Uq[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.