Deformations of Lie 2-algebras
Mathematical Physics
2015-06-16 v1 Category Theory
math.MP
Representation Theory
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 corresponds to a 2-cocycle of 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.
Keywords
Cite
@article{arxiv.1306.6225,
title = {Deformations of Lie 2-algebras},
author = {Zhangju Liu and Yunhe Sheng and Tao Zhang},
journal= {arXiv preprint arXiv:1306.6225},
year = {2015}
}
Comments
20 pages