Lie-isoclinism of pairs of Leibniz algebras

2018/07/25 by Zahra Riyahi, Riyahi, Zahra, José Manuel Casas Mirás +1
Mathematics · #17A32 #18B99 #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.1807.09446

openalex publication_date 2018/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The aim of this paper is to consider the relation between Lie-isoclinism and isomorphism of two pairs of Leibniz algebras. We show that, unlike the absolute case for finite dimensional Lie algebras, these concepts are not identical, even if the pairs of Leibniz algebras are Lie-stem. Moreover, throughout the paper we provide some conditions under which Lie-isoclinism and isomorphism of Lie-stem Leibniz algebras are equal. In order to get this equality, the concept of factor set is studied as well.

Citations

• Universal enveloping algebras of Leibniz algebras and (co)homology
• On non-abelian extensions of Leibniz algebras

Related

• On Lie-isoclinic Leibniz algebras
• A study of n-Lie-isoclinic Leibniz algebras
• Companion Lie Algebras of Leibniz Algebras
• Lattice isomorphisms of Leibniz algebras
• On some structures of Leibniz algebras