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arXiv · 1012.5515

Leibniz 2-algebras and twisted Courant algebroids

Yunhe Sheng·Zhangju Liu
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Abstract

In this paper, we give the categorification of Leibniz algebras, which is equivalent to 2-term sh Leibniz algebras. They reveal the algebraic structure of omni-Lie 2-algebras introduced in \cite{omniLie2} as well as twisted Courant algebroids by closed 4-forms introduced in \cite{4form}. We also prove that Dirac structures of twisted Courant algebroids give rise to 2-term $L_\infty$-algebras and geometric structures behind them are exactly $H$-twisted Lie algebroids introduced in \cite{Grutzmann}.

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Yunhe Sheng, Zhangju Liu. 2011-07-24. Leibniz 2-algebras and twisted Courant algebroids. https://doi.org/10.1080/00927872.2011.608201

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