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Quasi-hopf algebras associated withsl 2 and complex curves

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Abstract

We construct quasi-Hopf algebras quantizing double extensions of the Manin pairs of Drinfeld, associated to a curve with a meromorphic differential, and the Lie algebrasl 2. This construction makes use of an analysis of the vertex relations for the quantum groups obtained in our earlier work, PBW-type results and computation ofR-matrices for them; its key step is a factorization of the twist operator relating “conjugated” versions of these quantum groups.

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Authors and Affiliations

  1. Centre de Mathématiques, URA 169 du CNRS Ecole Polytechnique, 91128, Palaiseau, France

    Benjamin Enriquez

  2. FIM, HG G 45.1, ETH-Zentrum, Rämistr. 101, CH-8092, Zurich, Switzerland

    Benjamin Enriquez

  3. V.R.: Département de Mathématiques, Université d’Angers, 2, Bd. Lavoisier, 49045, Angers, France

    Vladimir Rubtsov

  4. ITEP, 25, Bol. Cheremushkinskaya, 117259, Moscow, Russia

    Vladimir Rubtsov

Authors
  1. Benjamin Enriquez
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  2. Vladimir Rubtsov
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Correspondence to Benjamin Enriquez.

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Enriquez, B., Rubtsov, V. Quasi-hopf algebras associated withsl 2 and complex curves. Isr. J. Math. 112, 61–108 (1999). https://doi.org/10.1007/BF02773478

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  • DOI: https://doi.org/10.1007/BF02773478

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