标题： SO(2N+1)李代数和Osp(1/2N)李超代数的量化与预振子生成元 显示英文标题

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

摘要： 李代数 $so(2n+1)$ 和李超代数 $osp(1/2n)$ 通过 $3n$ 生成元进行量子化，称为预振子生成元。 除了 $n$ “Cartan” 元素外，预振子生成元在 $so(2n+1)$的情况下是变形的拟费米算子，在 $osp(1/2n)$的情况下是变形的拟玻色算子。 对应的变形泛包络代数$U_q[so(2n+1)]$和$U_q[osp(1/2n)]$与用Chevalley算子定义的相同。 名称“预振子”是用来表明在某种表示中这些算子会简化为已知的变形费米和玻色算子。 显示英文摘要

摘要： 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.