English

On 3-Lie algebras with a derivation

Rings and Algebras 2021-10-12 v1

Abstract

In this paper, we study 3-Lie algebras with derivations. We call the pair consisting of a 3-Lie algebra and a distinguished derivation by the 3-LieDer pair. We define a cohomology theory for 3-LieDer pair with coefficients in a representation. We study central extensions of a 3-LieDer pair and show that central extensions are classified by the second cohomology of the 3-LieDer pair with coefficients in the trivial representation. We generalize Gerstenhaber's formal deformation theory to 3-LieDer pairs in which we deform both the 3-Lie bracket and the distinguished derivation.

Keywords

Cite

@article{arxiv.2110.04715,
  title  = {On 3-Lie algebras with a derivation},
  author = {Shuangjian Guo and Ripan Saha},
  journal= {arXiv preprint arXiv:2110.04715},
  year   = {2021}
}

Comments

18 pages. arXiv admin note: text overlap with arXiv:2003.07392 by other authors

R2 v1 2026-06-24T06:46:05.792Z