Deformations of 3-algebras

Abstract

We phrase deformations of n-Leibniz algebras in terms of the cohomology theory of the associated Leibniz algebra. We do the same for n-Lie algebras and for the metric versions of n-Leibniz and n-Lie algebras. We place particular emphasis on the case of n=3 and explore the deformations of 3-algebras of relevance to three-dimensional superconformal Chern--Simons theories with matter.

29 pages (V2: one error corrected: section 5.2 considerably shorter now)

References in corpus (6)

• Gauge Symmetry and Supersymmetry of Multiple M2-Branes
• Algebraic structures on parallel M2-branes
• Modeling Multiple M2's
• On the Lie-algebraic origin of metric 3-algebras
• Multiple M2-branes and Generalized 3-Lie algebras
• Superpotentials for superconformal Chern-Simons theories from representation theory

Cited by in corpus (9)

• Nijenhuis operators on $n$-Lie algebras
• A new approach to representations of $3$-Lie algebras and abelian extensions
• Twisted Rota-Baxter operators on 3-Lie algebras and NS-3-Lie algebras
• $3$-BiHom-Lie superalgebras induced by BiHom-Lie superalgebras
• On non-abelian extensions of 3-Lie algebras
• Deformations and cohomologies of embedding tensors on 3-Lie algebras
• Lie Algebroids in the Loday-Pirashvili Category
• Reynolds $n$-Lie algebras and NS-$n$-Lie algebras
• Deformations and extensions of modified $\lambda$-differential $3$-Lie Algebras