On the cohomology based on the generalized representations of n-Lie Algebras

2022/07/11 by Afi Maha, Maha, Afi, Sania Asif +5
Mathematics · #15A99 #16G30 #17A01 17B10 #17B56 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2207.04642

openalex publication_date 2022/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper, we define the new class of representation on n-Lie algebra that is called as generalized representation. We study the cohomology theory corresponding to generalized representations of n-Lie algebras and show its relation with the cohomology corresponding to the usual representations. Furthermore, we provide the computation for the low dimensional cocycles.

Related

• Cohomologies and generalized derivation extensions of n-Lie algebras
• Lie algebra of an n-Lie algebra
• Cohomology of n-Lie algebras in Loday-Pirashvili category
• Generalized representations of 3-Hom-Lie algebras
• A note on the cohomology of Lie algebras