The Schur Lie-Multiplier of Leibinz Algebras

2017/03/21 by J. M. Casas, Casas, J. M., Manuel A. Insua +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.1703.07148

openalex publication_date 2017/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a free presentation 0 → R → F → G → 0 of a Leibniz algebra G, the Baer invariant \cal M^{\sf Lie}(G) = \fracR ∩ [F, F]_Lie[F, R]_Lie is called the Schur multiplier of G relative to the Liezation functor or Schur Lie-multiplier. For a two-sided ideal N of a Leibniz algebra G, we construct a four-term exact sequence relating the Schur Lie-multiplier of G and G/N, which is applied to study and characterize Lie-nilpotency, Lie-stem covers and Lie-capability of Leibniz algebras.

Citations

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

Related

• The c-Nilpotent Shur Lie-Multiplier of Leibniz Algebras
• On the Schur Lie-multiplier and Lie-covers of Leibniz n-algebras
• Upper bounds on the dimension of the Schur Lie-multiplier of Lie-nilpotent Leibniz n-algebras
• Multipliers and Unicentral Leibniz Algebras
• On Lie-isoclinic Leibniz algebras