The Schur Lie-multiplier of Leibniz algebras

Abstract

For a free presentation 0 → τ → f → g → 0 of a Leibniz algebra g, the Baer invariant M^Lie(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.