Leibniz 2-Algebras and Twisted Courant Algebroids

DOI10.1080/00927872.2011.608201zbMath1337.17006arXiv1012.5515OpenAlexW2018450115MaRDI QIDQ5326270

Zhang-Ju Liu, Yun He Sheng

Publication date: 5 August 2013

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.5515

zbMATH Keywords

Dirac structureomni-Lie 2-algebrasLeibniz 2-algebrathe first Pontryagin classtwisted Courant algebroid

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Graded Lie (super)algebras (17B70) Pseudogroups and differentiable groupoids (58H05) Leibniz algebras (17A32)

Related Items (19)

3-Lie∞-algebras and 3-Lie 2-algebras ⋮ The Pontryagin class for pre-Courant algebroids ⋮ Hom-Leibniz 2-algebras ⋮ The first Pontryagin class of a quadratic Lie 2-algebroid ⋮ Contact Courant algebroids and \(L_\infty\)-algebras ⋮ A natural extension of the universal enveloping algebra functor to crossed modules of Leibniz algebras ⋮ Pre-Courant algebroids ⋮ Categorification of \(\mathsf{VB}\)-Lie algebroids and \(\mathsf{VB}\)-Courant algebroids ⋮ Omni-Lie 2-algebras and their Dirac structures ⋮ Crossed modules and non-abelian extensions of Rota-Baxter Leibniz algebras ⋮ Metric-Bourbaki algebroids: Cartan calculus for M-theory ⋮ Cohomology of hemistrict Lie 2-algebras ⋮ Leibniz bialgebras, relative Rota-Baxter operators, and the classical Leibniz Yang-Baxter equation ⋮ Higher algebra over the Leibniz operad ⋮ On non-abelian extensions of Leibniz algebras ⋮ Leibniz algebras with derivations ⋮ The controlling \(L_\infty \)-algebra, cohomology and homotopy of embedding tensors and Lie-Leibniz triples ⋮ Homotopy Poisson algebras, Maurer-Cartan elements and Dirac structures of CLWX 2-algebroids ⋮ Actor of a crossed module of dialgebras via tetramultipliers

Cites Work

• \(L _{\infty }\)-algebras from multisymplectic geometry
• Integration of twisted Poisson structures
• Semidirect products of representations up to homotopy
• Derived brackets and sh Leibniz algebras
• \(H\)-twisted Lie algebroids
• Omni-Lie 2-algebras and their Dirac structures
• Generalized complex geometry
• Coalgebraic approach to the Loday infinity category, stem differential for \(2n\)-ary graded and homotopy algebras
• The Lie algebra structure of tangent cohomology and deformation theory
• Courant algebroids and strongly homotopy Lie algebras
• Introduction to sh Lie algebras for physicists
• Universal enveloping algebras of Leibniz algebras and (co)homology
• Transitive Courant algebroids
• INTEGRATION OF SEMIDIRECT PRODUCT LIE 2-ALGEBRAS
• Crossed modules for Leibniz n-algebras
• On the geometric quantization of twisted Poisson manifolds
• First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-Form
• On weak Lie 2-algebras
• The first Pontryagin class

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