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Lie 2-Bialgebras

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Abstract

In this paper, we study Lie 2-bialgebras, paying special attention to coboundary ones, with the help of the cohomology theory of L ∞-algebras with coefficients in L ∞-modules. We construct examples of strict Lie 2-bialgebras from left-symmetric algebras (also known as pre-Lie algebras) and symplectic Lie algebras (also called quasi-Frobenius Lie algebras).

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Authors and Affiliations

  1. Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, 300071, China

    Chengming Bai

  2. Department of Mathematics, Jilin University, Changchun, 130012, Jilin, China

    Yunhe Sheng

  3. Courant Research Centre “Higher Order Structures”, Georg-August-University Göttingen, Bunsenstrasse 3-5, 37073, Göttingen, Germany

    Chenchang Zhu

Authors
  1. Chengming Bai
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  2. Yunhe Sheng
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  3. Chenchang Zhu
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Corresponding author

Correspondence to Yunhe Sheng.

Additional information

Communicated by Y. Kawahigashi

Research supported by NSFC (10920161, 11101179, 11271202), SRFDP (200800550015, 20100061120096) and the German Research Foundation (Deutsche Forschungsgemeinschaft (DFG)) through the Institutional Strategy of the University of Göttingen.

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Bai, C., Sheng, Y. & Zhu, C. Lie 2-Bialgebras. Commun. Math. Phys. 320, 149–172 (2013). https://doi.org/10.1007/s00220-013-1712-3

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