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

Abstract

Y 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(h)(1 vertical bar 2) and A(h')(2 vertical bar 1), 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 vertical bar 2). Finally, we get a new superalgebra derived from the Hopf superalgebra of functions on the quantum superspace A(p,q)(1 vertical bar 2).