Quaestiones Mathematicae

Log in or Register to get access to full text downloads.

Remember me or Register

DOWNLOAD FULL TEXT Open Access  DOWNLOAD FULL TEXT Subscription or Fee Access

The Schur Lie-multiplier of Leibniz algebras

J.M. Casas, M.A. Insua


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.
AJOL African Journals Online