Leibniz 2-algebras and twisted Courant algebroids
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 omniLie2 as well as twisted Courant algebroids by closed 4-forms introduced in 4form. We also prove that Dirac structures of twisted Courant algebroids give rise to 2-term L∞-algebras and geometric structures behind them are exactly H-twisted Lie algebroids introduced in Grutzmann.
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