On a Deformation of $sl(2)$ with Paragrassmannian Variables

Abstract

We propose a new structure ${\mathcal{U}}_q^r(sl(2))$. This is realized by multiplying $\delta$ ($q=e^{\delta }$, $δ\in \CC$) by $\theta$, where $\theta$ is a real nilpotent -paragrassmannian- variable of order $r$ (${\theta }^{r+1}=0$) that we call the order of deformation, the limit $r\to \infty$ giving back the standard ${\mathcal{U}}_q(sl(2))$. In particular we show that, for $r=1$, there exists a new $\mathcal{R}$-matrix associated with $sl(2)$. We also proof that the restriction of the values of the parameters of deformation give nonlinear algebras as particular cases.

12 pages, Latex-file, Minor change, To be published in J. Phys.A

References in corpus (1)

• On Nonlinear Angular Momentum Theories, Their Representations and Associated Hopf Structures

Cited by in corpus (2)

• Duality for Exotic Bialgebras
• On Linear Differential Equations Involving a Para-Grassmann Variable