On q - and h-deformations of 3d-superspaces
Yıl: 2021 Cilt: 45 Sayı: 1 Sayfa Aralığı: 346 - 359 Metin Dili: İngilizce DOI: 10.3906/mat-1907-80 İndeks Tarihi: 06-07-2022
On q - and h-deformations of 3d-superspaces
Öz: 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 .
Anahtar Kelime: Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
- [1] Aghamohammadi A, Khorrami M, Shariati A. h-deformation as a contraction of q -deformation. Jordanian deformation of SL(2) as a contraction of its Drinfeld-Jimbo deformation. Journal of Physics A: Mathematical and General 1995; 28 (8): L225-L231.
- [2] Celik S. Two-parametric extension of h-deformation of GL(1|1). Letters in Mathematical Physics 1997; 42: 299-308.
- [3] Celik S. Differential geometry of the Lie algebra of the quantum superplane. Balkan Physics Letters 2003; 11: 119-127. (arXiv:math/0201170)
- [4] Celik S. Bicovariant differential calculus on the quantum superspace Rq(1|2). Journal of Algebra and its Applications 2016; 15: 1650172 (17 pages).
- [5] Celik Sultan A. Differential calculi on super-Hopf algebra F(Rq(1|2)). Advanced in Applied Clifford Algebras 2018; 28: 85:1-16.
- [6] Celik Sultan A. A two-parameter deformation of supergroup GL(1|2). Journal of the Institute of Science and Technology 2018; 8(4): 271-280.
- [7] Dabrowski L, Parashar P. h-deformation of GL(1|1). Letters in Mathematical Physisc 1996; 38: 331-336.
- [8] Faddeev LD, Reshetikhin NY, Takhtajan LA. Quantization of Lie groups and Lie algebras. Leningrad Mathematical Journal 1990; 1 (1): 193-225.
- [9] Kupershmidt BA. The quantum group GL h(2). Journal of Physics A: Mathematical and General 1992; 25: L1239- L1244.
- [10] Manin YI. Quantum groups and noncommutative geometry. Montreal, Canada: Centre de Recherches Mathematiques, Universite de Montreal, 1988.
- [11] Manin YI. Multiparametric quantum deformation of the general linear supergroup. Communications in Mathematical Physics 1989; 123 (1): 163-175.
- [12] Woronowicz SL. Differential calculus on compact matrix pseudogroups (quantum groups). Communications in Mathematical Physics 1989; 122 (1): 125-170.
| APA | celik s (2021). On q - and h-deformations of 3d-superspaces . , 346 - 359. 10.3906/mat-1907-80 |
| Chicago | celik salih On q - and h-deformations of 3d-superspaces . (2021): 346 - 359. 10.3906/mat-1907-80 |
| MLA | celik salih On q - and h-deformations of 3d-superspaces . , 2021, ss.346 - 359. 10.3906/mat-1907-80 |
| AMA | celik s On q - and h-deformations of 3d-superspaces . . 2021; 346 - 359. 10.3906/mat-1907-80 |
| Vancouver | celik s On q - and h-deformations of 3d-superspaces . . 2021; 346 - 359. 10.3906/mat-1907-80 |
| IEEE | celik s "On q - and h-deformations of 3d-superspaces ." , ss.346 - 359, 2021. 10.3906/mat-1907-80 |
| ISNAD | celik, salih. "On q - and h-deformations of 3d-superspaces ". (2021), 346-359. https://doi.org/10.3906/mat-1907-80 |
| APA | celik s (2021). On q - and h-deformations of 3d-superspaces . Turkish Journal of Mathematics, 45(1), 346 - 359. 10.3906/mat-1907-80 |
| Chicago | celik salih On q - and h-deformations of 3d-superspaces . Turkish Journal of Mathematics 45, no.1 (2021): 346 - 359. 10.3906/mat-1907-80 |
| MLA | celik salih On q - and h-deformations of 3d-superspaces . Turkish Journal of Mathematics, vol.45, no.1, 2021, ss.346 - 359. 10.3906/mat-1907-80 |
| AMA | celik s On q - and h-deformations of 3d-superspaces . Turkish Journal of Mathematics. 2021; 45(1): 346 - 359. 10.3906/mat-1907-80 |
| Vancouver | celik s On q - and h-deformations of 3d-superspaces . Turkish Journal of Mathematics. 2021; 45(1): 346 - 359. 10.3906/mat-1907-80 |
| IEEE | celik s "On q - and h-deformations of 3d-superspaces ." Turkish Journal of Mathematics, 45, ss.346 - 359, 2021. 10.3906/mat-1907-80 |
| ISNAD | celik, salih. "On q - and h-deformations of 3d-superspaces ". Turkish Journal of Mathematics 45/1 (2021), 346-359. https://doi.org/10.3906/mat-1907-80 |
