Differential geometry of the Lie algebra of the quantum plane

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Apr 2005Embargo end date: 01 Jan 2003 Turkey English Publisher:Springer Science and Business Media LLCJournal:Czechoslovak Journal of Physics, volume 55, pages 463-471 (issn: 0011-4626, eissn: 1572-9486,

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Authors: ÇELİK, Salih; ÇELİK, Sultan;

doi: 10.1007/s10582-005-0052-8 , 10.48550/arxiv.math/0304385

arXiv: math/0304385

Differential geometry of the Lie algebra of the quantum plane

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Abstract

We present a differential calculus on the extension of the quantum plane obtained considering that the (bosonic) generator $x$ is invertible and furthermore working polynomials in $\ln x$ instead of polynomials in $x$. We call quantum Lie algebra to this extension and we obtain its Hopf algebra structure and its dual Hopf algebra. Differential geometry of the quantum Lie algebra of the extended quantum plane and its Hopf algebra structure is obtained. Its dual Hopf algebra is also given.

11 pages, no fiqures

Country

Turkey

Related Organizations

Yıldız Technical University
Turkey
YILDIZ TECNHICAL UNIVERSITY
Turkey

Keywords

Mathematics - Differential Geometry, Differential Geometry (math.DG), 16W30; 58B32, Mathematics - Quantum Algebra, 58B32, FOS: Mathematics, Quantum Algebra (math.QA), 16W30

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Differential geometry of the quantum 3-dimensional space
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