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Drinfeld and Jimbo’s Quantum Enveloping Algebras

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Quantum Groups

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

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Abstract

In Part I we have investigated at length the quantum enveloping alge-bra of sl(2). In this chapter we give a brief presentation of the algebras Uh(g) associated by Drinfeld [Dri85][Dri87] and Jimbo [Jim85] to the other semisimple Lie algebras g. The algebras Uh(g) provide non-trivial examples of quantum enveloping algebras as defined in XVI.5 as well as examples of isotopy invariants of links. We shall also need Uh(g) in Chapter XIX to state the Drinfeld-Kohno theorem on the monodromy of the Knizhnik-Zamolodchikov systems. Finally, in Section 4 we shall determine an explicit universal R-matrix for the quantum enveloping algebra of sl(2), using the crossed bimodules of IX.5.

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© 1995 Springer Science+Business Media New York

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Kassel, C. (1995). Drinfeld and Jimbo’s Quantum Enveloping Algebras. In: Quantum Groups. Graduate Texts in Mathematics, vol 155. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0783-2_17

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  • DOI: https://doi.org/10.1007/978-1-4612-0783-2_17

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6900-7

  • Online ISBN: 978-1-4612-0783-2

  • eBook Packages: Springer Book Archive

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