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Quaestiones Mathematicae

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The Schur Lie-multiplier of Leibniz algebras

J.M. Casas, M.A. Insua

Abstract


For a free presentation 0 → τ → f → g → 0 of a Leibniz algebra g, the Baer invariant MLie(g) = τ∩[f;f]Lie/[f;τ]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-multipliers of g and g/n, which is applied to study and characterize Lie-nilpotency, Lie-stem covers and Lie-capability of Leibniz algebras.

Mathematics Subject Classication (2010): 17A32, 18B99.

Key words: Lie-central extension, Schur Lie-multiplier, Lie-nilpotent Leibniz algebra, Lie-
stem cover.




http://dx.doi.org/10.2989/16073606.2017.1417335
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