A Two-Parameter Quantum (2+1)-Superspace and its Deformed Derivation Algebra as Hopf Superalgebra

Özavşar, Muttalip

doi:10.1007/s00006-013-0394-4

Cited by 3 publications

(1 citation statement)

References 36 publications

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“…The first description of Manin's quantum plane as a Hopf algebra is by Tahri [36]. For quantisations of various superspaces and their corresponding differential calculi see [10,11,23,32,35]. Nontrivial actions of quantized universal enveloping algebras on the quantum plane were considered in [22].…”

Section: Introductionmentioning

confidence: 99%

Double-graded quantum superplane

Bruce,

Duplij

2019

Preprint

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A Z 2 × Z 2 -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 commutation rules between the coordinates, their differentials and partial derivatives are explicitly given. Furthermore, we show that an extended version of the double-graded quantum superplane admits a natural Hopf Z 2 2 -algebra structure.

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Section: Introductionmentioning

confidence: 99%

Double-graded quantum superplane

Bruce,

Duplij

2019

Preprint

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Double-Graded Quantum Superplane

Bruce

Duplij

2020

Reports on Mathematical Physics

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Left-covariant first order differential calculus on quantum Hopf supersymmetry algebra

Fakhri

Laheghi

2021

Journal of Mathematical Physics

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We introduce a Hopf algebra structure on the N = 2 quantum supersymmetry algebra and formulate a first order quantum differential calculus on it. Then, it is enhanced to three *-calculi by defining three appropriate involution maps on the quantum super-algebra. Two of the *-structures correspond to quantum complex super-algebra and the other correspond to a quantum real one. An appropriate quantum super-Hopf algebra including two even and two odd generators and also its corresponding quantum super-group are introduced. Compared to the quantum super-algebra, the quantum super-group also has three different *-structures. It is shown that the differential calculus over the quantum super-algebra is left-covariant with respect to the quantum super-group. Besides, it is shown that the graded differential algebra for the case q = 1 is a bicovariant bimodule over the undeformed Hopf supersymmetry algebra.

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A Two-Parameter Quantum (2+1)-Superspace and its Deformed Derivation Algebra as Hopf Superalgebra

Cited by 3 publications

References 36 publications

Double-graded quantum superplane

Double-graded quantum superplane

Double-Graded Quantum Superplane

Left-covariant first order differential calculus on quantum Hopf supersymmetry algebra

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