Bicovariant differential calculus on the superspace ${\mathbb R}_q(1|2)$
Salih Celik
TL;DR
This paper develops a bicovariant differential calculus on the quantum superspace ${\mathbb R}_q(1|2)$, constructing related algebraic structures and identifying a new quantum supergroup as its symmetry.
Contribution
It introduces a novel bicovariant differential calculus on the quantum superspace and explicitly constructs the associated quantum Lie superalgebra and symmetry supergroup.
Findings
Super Hopf algebra structure defined on the function algebra.
Bicovariant differential calculus established on the superspace.
A new quantum supergroup symmetry identified.
Abstract
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.
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