On q - and h-deformations of 3d-superspaces

Abstract

In this paper, we introduce nonstandard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces are denoted by A 1|2 h and A 2|1 h′ , respectively. We find a two-parameter R-matrix satisfying quantum Yang–Baxter equation and thus obtain a new two-parameter nonstandard deformation of the supergroup GL(1|2). Finally, we get a new superalgebra derived from the Hopf superalgebra of functions on the quantum superspace A 1|2 p,q .