Covariant Differential Calculi on $SP_q^{1|2}$

TL;DR

This paper introduces a quantum supergroup, develops covariant differential calculi on a quantum superspace, and explores deformations of symplectic superspaces and the Heisenberg superalgebra, advancing quantum supergeometry.

Contribution

It presents new covariant differential calculi on $SP_q^{1|2}$ and introduces an $h$-deformation of the Heisenberg superalgebra, expanding the framework of quantum supergeometry.

Findings

Introduces a unitary orthosymplectic quantum supergroup.

Provides two covariant differential calculi on $SP_q^{1|2}$.

Derives $h$-deformed symplectic superspaces and a new $h$-deformation of the Heisenberg superalgebra.

Abstract

A unitary orthosymplectic quantum supergroup is introduced. Two covariant differential calculi on the quantum superspace $SP_q^{1|2}$ are presented. The $h$-deformed symplectic superspaces via a contraction of the $q$-deformed symplectic superspaces are obtained. A new $h$-deformation of the Heisenberg superalgebra is given.