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

Authors: SALİH ÇELİK

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 ${\mathbb A}_h^{1|2}$ and ${\mathbb A}_{h'}^{2|1}$, 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 ${\rm GL}(1|2)$. Finally, we get a new superalgebra derived from the Hopf superalgebra of functions on the quantum superspace ${\mathbb A}_{p,q}^{1|2}$.

Keywords: Quantum superspace, Hopf superalgebra, quantum supergroup, quantum Lie superalgebra, super $\star$-algebra

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