On $q$- and $h$-deformations of 3d-superspace

Abstract

In this paper, we introduce non-standard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces denoted by ${\mathbb{A}}_h^{1|2}$ and ${\mathbb{A}}_{h^{\prime }}^{2|1}$, respectively. We find a two-parameter $R$-matrix satisfying quantum Yang-Baxter equation and thus obtain a {\it new} two-parameter non-standard deformation of the supergroup $\mathrm{GL}(1|2)$. Finally, we get a new superalgebra derived from the super-Hopf algebra of functions on the quantum superspace ${\mathbb{A}}_{p,q}^{1|2}$.

14 pages

References in corpus (5)

• Dictionary on Lie Superalgebras
• $h$-Deformation as a Contraction of $q$-Deformation
• h-deformation of GL(1|1)
• Differential Geometry of the Lie superalgebra of the quantum superplane
• Two-parametric extension of h-deformation of GL$(1|1)$