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 \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}.

22 pages, to appear in Comm. Algebra

References in corpus (5)

• Generalised Geometry for M-Theory
• On weak Lie 2-algebras
• H-twisted Lie algebroids
• Omni-Lie 2-algebras and their Dirac structures
• H-twisted Courant algebroids

Cited by in corpus (18)

• The Pontryagin Class for Pre-Courant Algebroids
• The controlling $L_{\infty }$-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples
• Pre-Courant Algebroids
• Omni-Lie 2-algebras and their Dirac structures
• Twisted Courant algebroids and coisotropic Cartan geometries
• H-twisted Courant algebroids
• Cohomology for almost Lie algebroids
• Courant Algebroids in Parabolic Geometry
• Extension, deformation and categorification of $\text{AssDer}$ pairs
• The first Pontryagin class of a quadratic Lie 2-algebroid
• Cohomology of hemistrict Lie 2-algebras
• Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids
• Dirac and Generalized Complex Structures on Cartan Geometries
• H-standard cohomology for Courant-Dorfman algebras and Leibniz algebras
• Contact Courant algebroids and $L_{\infty }$-algebras
• A natural extension of the universal enveloping algebra functor to crossed modules of Leibniz algebras
• On non-abelian extensions of Leibniz algebras
• Categorification of VB-Lie algebroids and VB-Courant algebroids