Basic Twist Quantization of osp(1|2) and kappa-- Deformation of D=1 Superconformal Mechanics

TL;DR

This paper presents a detailed construction of a nonstandard quantum deformation of osp(1|2), including explicit twisting functions, coproducts, and R-matrices, and explores its application as a symmetry algebra in superconformal mechanics.

Contribution

It provides the explicit form of the twisting function, coproducts, and R-matrix for a super-Jordanian quantum deformation of osp(1|2), and interprets one real form as a kappa-deformation relevant to superconformal mechanics.

Findings

Explicit twisting function for osp(1|2) deformation

Construction of quantum coproducts and R-matrix

Application to superconformal mechanics symmetry

Abstract

The twisting function describing a nonstandard (super-Jordanian) quantum deformation of $osp(1|2)$ is given in explicite closed form. The quantum coproducts and universal R-matrix are presented. The non-uniqueness of the twisting function as well as two real forms of the deformed $osp(1|2)$ superalgebras are considered. One real quantum $osp(1|2)$ superalgebra is interpreted as describing the $\kappa$-deformation of D=1, N=1 superconformal algebra, which can be applied as a symmetry algebra of N=1 superconformal mechanics.