On the capablility of Hom-Lie algebras

2021/01/27 by J. M. Casas, Casas, José Manuel, Xabier García‐Martínez +1
Mathematics · #17B61 #18G50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.2101.11522

openalex publication_date 2021/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Hom-Lie algebra (L, α_L) is said to be capable if there exists a Hom-Lie algebra (H, α_H) such that L ≅ H/Z(H). We obtain a characterisation of capable Hom-Lie algebras involving its epicentre and we use this theory to further study the six-term exact sequence in homology and to obtain a Hopf-type formulae of the second homology of perfect Hom-Lie algebras.

Related

• The exterior product and homology of Hom-Lie algebras
• On Hom-algebra structures
• Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras
• Complex and Kahler structures on hom-Lie algebras
• On Hom–Lie algebras