Deformations of Lie 2-algebras

Abstract

In this paper, we consider deformations of Lie 2-algebras via the cohomology theory. We prove that a 1-parameter infinitesimal deformation of a Lie 2-algebra $\g$ corresponds to a 2-cocycle of $\g$ with the coefficients in the adjoint representation. The Nijenhuis operator for Lie 2-algebras is introduced to describe trivial deformations. We also study abelian extensions of Lie 2-algebras from the viewpoint of deformations of semidirect product Lie 2-algebras.

20 pages

References in corpus (4)

• Poisson Quasi-Nijenhuis Manifolds
• Lie 2-bialgebras
• Non-abelian Extensions of Lie 2-algebras
• Nijenhuis forms on $L_{\infty }$-algebras and Poisson geometry

Cited by in corpus (6)

• Cohomological characterizations of non-abelian extensions of strict Lie 2-algebras
• Split Courant algebroids as $L_{\infty }$-structures
• A cohomological proof for the integrability of strict Lie 2-algebras
• A cohomology theory for Lie 2-algebras
• Nijenhuis forms on $L_{\infty }$-algebras and Poisson geometry
• Cohomology of hemistrict Lie 2-algebras