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Nonabelian omni-Lie algebras

Volume 110 / 2016

Honglei Lang, Yunhe Sheng, Xiaomeng Xu Banach Center Publications 110 (2016), 167-176 MSC: Primary 17B99; Secondary 53D17. DOI: 10.4064/bc110-0-11


We introduce the notion of a nonabelian omni-Lie algebra associated to a Lie algebra. From a geometric point of view, it is the linearization of the Courant algebroid associated to a Poisson manifold. As an algebraic application, we show that its Dirac structures describe deformations of the Lie algebra.


  • Honglei LangDepartment of Mathematics and LMAM
    Peking University
    Beijing 100871, China
  • Yunhe ShengDepartment of Mathematics
    Jilin University
    Changchun 130012, China
  • Xiaomeng XuSection of Mathematics
    University of Geneva
    2-4 Rue de Lièvre, c.p. 64
    4, Switzerland

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