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Multi-brace cotensor Hopf algebras and quantum groups

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Abstract

We give a construction of the whole quantum group associated to a symmetrizable Kac-Moody Lie algebra as a quantum quasi-symmetric algebra, a particular case of multi-brace cotensor Hopf algebras, in the spirit of the quantum shuffle construction of the “plus part”. All highest weight irreducible representations are constructed using this machinery. It also provides a systematic way to construct simple modules over the quantum double of a quantum group.

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Authors and Affiliations

  1. Mathematisches Institut, Universität zu Köln, Weyertal 86-90, 50931, Cologne, Germany

    Xin Fang

  2. Institut de Mathématiques de Jussieu - Paris Rive Gauche, Université Paris Diderot-Paris VII, Bâtiment Sophie Germain, Case 7012, 75205, Paris Cedex 13, France

    Marc Rosso

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  1. Xin Fang
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  2. Marc Rosso
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Correspondence to Xin Fang.

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Fang, X., Rosso, M. Multi-brace cotensor Hopf algebras and quantum groups. Math. Z. 286, 657–678 (2017). https://doi.org/10.1007/s00209-016-1777-8

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  • DOI: https://doi.org/10.1007/s00209-016-1777-8

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