2021/10/10 by Shuangjian Guo, Guo, Shuangjian, Ripan Saha +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2110.04715
openalex publication_date 2021/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.