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

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Abstract

As is well known, a Hopf algebra setting is an efficient tool to study some geometric structures such as the Maurer-Cartan invariant forms and the corresponding vector fields on a noncommutative space. In this study we introduce a two-parameter quantum (2+1)-superspace with a Hopf superalgebra structure.We also define some derivation operators acting on this quantum superspace, and we show that the algebra of these derivations is a Hopf superalgebra. Furthermore it will be shown how the derivation operators lead to a bicovariant differential calculus on the two- parameter quantum (2+1)-superspace. In conclusion, based on the bicovariant differential calculus, the Maurer-Cartan right invariant differential forms and the corresponding quantum Lie superalgebra are given.

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  1. Department of Mathematics, Yildiz Technical University, Davutpasa-Esenler, P.O. Box 34210, Turkey

    Muttalip Özavşar

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  1. Muttalip Özavşar
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Özavşar, M. A Two-Parameter Quantum (2+1)-Superspace and its Deformed Derivation Algebra as Hopf Superalgebra. Adv. Appl. Clifford Algebras 23, 741–756 (2013). https://doi.org/10.1007/s00006-013-0394-4

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  • DOI: https://doi.org/10.1007/s00006-013-0394-4

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