Hopf algebra structure on superspace $\text{SP}_q^{2|1}$

Year 2020, , 777 - 783, 02.04.2020

Salih Celik

https://doi.org/10.15672/hujms.499848

Abstract

Super-Hopf algebra structure on the function algebra on the extended quantum symplectic superspace $\text{SP}_q^{2|1}$, denoted by ${\mathbb F}({\text{SP}}_q^{2|1})$, is defined. A quantum Lie superalgebra derived from ${\mathbb F}({\text{SP}}_q^{2|1})$ is explicitly obtained.

Keywords

Quantum symplectic superspace, super $\star$-algebra, super-Hopf algebra, quantum supergroup

References

• [1] A. Aghamohammadi, M. Khorrami, and A. Shariati, h-deformation as a contraction of q-deformation, J. Phys. A: Math. Gen. 28, L225-L231, 1995.
• [2] N. Aizawa and R. Chakrabarti, Quantum Spheres for $OSP_q(1|2)$, J. Math. Phys. 46, 103510:1-25, 2005.
• [3] S. Celik, Covariant differential calculi on quantum symplectic superspace ${\text{SP}}_q^{1|2}$, J.Math. Phys. 58, 023508:1-15, 2017.
• [4] M. Chaichian and P.P. Kulish, Quantum group covariant systems, in From field theory to quantum groups. World Sci. Publ., River Edge, NJ, 99-111, 1996.
• [5] L.D. Faddeev, N.Yu. Reshetikhin, and L.A. Takhtajan, Quantization of Lie groups and Lie algebras, Leningrad Math. J. 1, 193-225, 1990.
• [6] P.P. Kulish and N.Yu Reshetikhin, Universal R-matrix of the quantum superalgebra $osp(2|1)$, Lett. Math. Phys. 18, 143-149, 1989.
• [7] Yu I. Manin, Multiparametric quantum deformation of the general linear supergroup, Commun. Math. Phys. 123, 163-175, 1989.