Ado theorem for nilpotent Hom–Lie algebras

2018/07/31 by Abdenacer Makhlouf, Pasha Zusmanovich
Mathematics · #Adjoint representation of a Lie algebra #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Discrete mathematics #Lie algebra #Lie conformal algebra #Mathematics #Nilpotent #Nilpotent group #Pure mathematics #Representation (politics) #Representation theorem #Representation theory #math.RA #math.RT #msc:16G99 #msc:17A99 #msc:17B01 #msc:17B10 #msc:17B30

paper · pdf · doi:10.1142/s0218196719500528

published as International Journal of Algebra and Computation 29 (2019), no.7, 1343-1365 · 16 pages; to appear in Intern. J. Algebra Comp.; v2: minor changes

openalex publication_date 2019/06/12 · arxiv created 2019/07/08 · arxiv updated 2019/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove an analog of the Ado theorem — the existence of a finite-dimensional faithful representation — for a certain kind of finite-dimensional nilpotent Hom–Lie algebras.

Citations

• The Mikheev identity in right Hom-alternative algebras
• Notes on Formal Deformations of Hom-associative and Hom-Lie Algebras
• A Note on Automorphisms and Derivations of Lie Algebras
• On Hom–Lie algebras
• Representability of Lie Algebras and Lie Groups by Matrices