Original scientific paper

Cartan calculus on the superalgebra ${\cal O}({\mathbb C}_q^{2\vert1})$

Salih Çelik orcid.org/0000-0002-6590-1032 ; Department of Mathematics, Yildiz Technical University, Istanbul, Turkey

Abstract

In analogy with the classical case, the noncommutative differential calculus on a quantum superspace can be extended to the Cartan calculus by introducing inner derivations and Lie derivatives. So, to give a Cartan calculus on the algebra of functions on quantum (2+1)-superspace ${\mathbb C}_q^{2\vert1}$, we first introduce two left-covariant differential calculi over ${\cal O}({\mathbb C}_q^{2\vert1})$ and extend one of these calculi by adding inner derivations and Lie derivatives to the calculus. We also introduce tensor product realization of the wedge product of forms.

Keywords

Quantum superspaces, Hopf superalgebra, Differential calculus, Clifford superalgebra, Inner derivation, Lie derivative, Cartan calculus.

Hrčak ID:

308962

URI

https://hrcak.srce.hr/308962

Publication date:

22.10.2023.

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