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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 \g\g corresponds to a 2-cocycle of \g\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.

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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}
}

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20 pages