# Bicovariant differential calculus on the quantum superspace ℝq(1|2)

@article{Celik2015BicovariantDC, title={Bicovariant differential calculus on the quantum superspace ℝq(1|2)}, author={Salih Celik}, journal={Journal of Algebra and Its Applications}, year={2015}, volume={15}, pages={1650172} }

Super-Hopf algebra structure on the function algebra on the extended quantum superspace has been defined. It is given a bicovariant differential calculus on the superspace. The corresponding (quantum) Lie superalgebra of vector fields and its Hopf algebra structure are obtained. The dual Hopf algebra is explicitly constructed. A new quantum supergroup that is the symmetry group of the differential calculus is found.

## 13 Citations

### Covariant differential calculi on quantum symplectic superspace S P q 1 | 2

- Physics, Mathematics
- 2017

A unitary orthosymplectic quantum supergroup is introduced. Two covariant differential calculi on the quantum superspace S P q 1 | 2 are presented. The h-deformed symplectic superspaces via a…

### A Differential Calculus on Superspace $${{\mathbb R}_h(1|2)}$$Rh(1|2) and Related Topics

- Mathematics
- 2017

We present a noncommutative differential calculus on the h-superspace via a contraction of the q-superspace, and find a new quantum matrix superalgebra. We also give a new deformation of the…

### Q A ] 2 5 A ug 2 02 0 DOUBLE-GRADED QUANTUM SUPERPLANE

- Mathematics
- 2020

A Z2 × Z2-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the double-graded quantum superplane. The…

### Q A ] 2 0 O ct 2 01 9 DOUBLE-GRADED QUANTUM SUPERPLANE

- Mathematics, Physics
- 2019

A Z2 × Z2-graded generalisation of the quantum superplane is proposed and studied. We construct a bicovariant calculus on what we shall refer to as the double-graded quantum superplane. The…

### N ov 2 01 8 On qand h-deformations of 3 d-superspace

- Mathematics
- 2018

In this paper, we introduce non-standard deformations of (1+2)and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces denoted by A 1|2 h and A 2|1 h ,…

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

- Mathematics
- 2018

In this paper, we introduce non-standard deformations of (1+2)- and (2+1)-superspaces via a contraction using standard deformations of them. This deformed superspaces denoted by ${\mathbb A}_h^{1|2}$…

### A Two-parameter Deformation of Supergroup GL(1|2)

- PhysicsJournal of the Institute of Science and Technology
- 2018

Kuantum Yang-Baxter denkleminin cozumu olan bir R-matrisi yardimiyla, standard RTT-bagintisi kullanilarak ile gosterilen yeni bir super-Hopf cebiri elde edilmistir.

### Quantum de Rham complex on 𝔸h1|2

- Mathematics, GeologyJournal of Algebra and Its Applications
- 2019

Introducing [Formula: see text]- and [Formula: see text]-deformations of [Formula: see text]-graded ([Formula: see text])- and ([Formula: see text])-spaces, denoted by [Formula: see text] and…

### Differential Calculi on Super-Hopf Algebra $$\mathsf{F}\varvec{(}{\mathbb {R}}_{\varvec{q}}\varvec{(1|2))}$$F(Rq(1|2))

- MathematicsAdvances in Applied Clifford Algebras
- 2018

It is constructed two-parameter left-covariant differential calculi on the function algebra on $${\mathbb {R}}_q(1|2)$$Rq(1|2) with respect to super-Hopf algebra…

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