The Two-Parameter Higher Order Differential Calculus and Curvature on a Quantum Plane

M. El Baz; A. El Hassouni; Y. Hassouni; E. H. Zakkari

The Two-Parameter Higher Order Differential Calculus and Curvature on a Quantum Plane

High Energy Physics - Theory 2007-05-23 v1

Authors: M. El Baz , A. El Hassouni , Y. Hassouni , E. H. Zakkari

Abstract

We construct an associative differential algebra on a two-parameter quantum plane associated with a nilpotent endomorphism $d$ in the two cases $d^{2}=0$ and $d^3=0$ $(d^2\neq 0).$ The correspondent curvature is derived and the related non commutative gauge field theory is introduced.

Keywords

quantum algebra deformation quantization diffeomorphism invariance in gravity

Cite

@article{arxiv.hep-th/0312239,
  title  = {The Two-Parameter Higher Order Differential Calculus and Curvature on a Quantum Plane},
  author = {M. El Baz and A. El Hassouni and Y. Hassouni and E. H. Zakkari},
  journal= {arXiv preprint arXiv:hep-th/0312239},
  year   = {2007}
}

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11 pages

The Two-Parameter Higher Order Differential Calculus and Curvature on a Quantum Plane

Abstract

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