On Nonstandard Quantizations of osp(2|1) Superalgebra via Contraction and Mapping

Abstract

We develop a generic reprersentation-independent contraction procedure for obtaining, for instance, $R_{\mathsf{h}}$ and $L$ operators of arbitrary dimensions for the quantized ${\mathcal{U}}_{\mathsf{h}}(osp(2|1))$ algebra corresponding to the classical $r_2$ matrix from the pertinent quantities of the standard q-deformed ${\mathcal{U}}_q(osp(2|1))$ algebra. Also the quantized ${\mathbf{U}}_{\mathbf{h}}(osp(2|1))$ algebra corresponding to the classical $r_1$ matrix comprising of the generators of the classical $sl(2)$ algebra is obtained in terms of a nonlinear basis set.

13 pages