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.
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