A cohomological characterization of Leibniz central extensions of Lie algebras

2006/05/31 by Naihong Hu, Yufeng Pei, Dong Liu · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #math.RA #msc:17A32 #msc:17B56 #msc:17B65

paper · pdf · doi:10.1090/s0002-9939-07-08985-x

published as Proc. Amer. Math. Soc. 136 (2), (2008), 437--447 · 12 pages. Proc. Amer.Math.Soc. (to appear in a simplified version)

arxiv created 2006/10/28 · openalex publication_date 2007/10/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Mainly motivated by Pirashvili’s spectral sequences on a Leibniz algebra, a cohomological characterization of Leibniz central extensions of Lie algebras is given. In particular, as applications, we obtain the cohomological version of Gao’s main theorem for Kac-Moody algebras and answer a question in an earlier paper by Liu and Hu (2004).

Citations

• Universal enveloping algebras of Leibniz algebras and (co)homology

Cited by

• On a class of n-Leibniz deformations of the simple Filippov algebras