# Introduction to quantum algebras

Abstract : The concept of a quantum algebra is made easy through the investigation of the prototype algebras $u_{qp}(2)$, $su_q(2)$ and $u_{qp}(1,1)$. The latter quantum algebras are introduced as deformations of the corresponding Lie algebras~; this is achieved in a simple way by means of $qp$-bosons. The Hopf algebraic structure of $u_{qp}(2)$ is also discussed. The basic ingredients for the representation theory of $u_{qp}(2)$ are given. Finally, in connection with the quantum algebra $u_{qp}(2)$, we discuss the $qp$-analogues of the harmonic oscillator and of the (spherical and hyperbolical) angular momenta.
Type de document :
Communication dans un congrès
International School Of Theoretical Physics Symmetry And Structural Properties Of Condensed Matter 2, Aug 1992, Poznan, Poland. World Scientific, pp.1-24, 1993
Domaine :

http://hal.in2p3.fr/in2p3-00002501
Contributeur : Sylvie Flores <>
Soumis le : jeudi 23 novembre 2006 - 11:26:05
Dernière modification le : mercredi 27 juillet 2016 - 14:48:48

### Citation

M. Kibler. Introduction to quantum algebras. International School Of Theoretical Physics Symmetry And Structural Properties Of Condensed Matter 2, Aug 1992, Poznan, Poland. World Scientific, pp.1-24, 1993. <in2p3-00002501>

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