Turkish Journal of Mathematics
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 ${\mathbb A}_{p,q}^{1 2}$.
DOI
10.3906/mat-1907-80
Keywords
Quantum superspace, Hopf superalgebra, quantum supergroup, quantum Lie superalgebra, super $\star$-algebra
First Page
346
Last Page
359
Recommended Citation
ÇELİK, SALİH
(2021)
"On $q$- and $h$-deformations of 3d-superspaces,"
Turkish Journal of Mathematics: Vol. 45:
No.
1, Article 21.
https://doi.org/10.3906/mat-1907-80
Available at:
https://journals.tubitak.gov.tr/math/vol45/iss1/21
