Quantum Groups pp 121-139 | Cite as

The Quantum Enveloping Algebra of sl(2)

Part of the Graduate Texts in Mathematics book series (GTM, volume 155)


The aim of Chapters VI-VII is to construct a Hopf algebra Uq = Uq (sl(2)) which is a one-parameter deformation of the enveloping algebra of the Lie algebra sl(2) investigated in Chapter V, and which is in duality with the Hopf algebra SLq(2) defined in Chapter IV. It will be our second main example of a quantum group. When the parameter q is not a root of unity, the algebra Uq has properties parallel to those of the enveloping algebra of sl(2). In the present chapter we classify the simple finite-dimensional modules of Uq and determine its centre. We close the chapter with a few considerations on the case when q is a root of unity.


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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  1. 1.Institut de Recherche Mathématique AvancéeUniversité Louis Pasteur-C.N.R.S.StrasbourgFrance

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