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Double Yangian and the universal R-matrix

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Abstract

We describe the double Yangian of the general linear Lie algebra glN by following a general scheme of Drinfeld. We also describe the centre of the Yangian by using its Hopf algebra structure, and provide a proof of the analogue of the Poincaré—Birkhoff—Witt theorem for the Yangian based on its representation theory. This proof extends to the double Yangian.

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Authors and Affiliations

  1. Department of Mathematics, University of York, York, YO10 5DD, UK

    Maxim Nazarov

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  1. Maxim Nazarov
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Communicated by: Yasuyuki Kawahigashi

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Nazarov, M. Double Yangian and the universal R-matrix. Jpn. J. Math. 15, 169–221 (2020). https://doi.org/10.1007/s11537-019-1912-5

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  • DOI: https://doi.org/10.1007/s11537-019-1912-5

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