Review

The Schur Lie-multiplier of Leibniz algebras

Published in: Quaestiones Mathematicae
Volume 41 , issue 7 , 2018 , pages: 917–936

DOI: 10.2989/16073606.2017.1417335

Author(s): J.M. Casas Dpto. Matemática Aplicada, Spain , M.A. Insua Dpto. Matemática Aplicada, Spain

Keywords: 17A32 , 18B99 , 17A32 , 18B99

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Abstract

For a free presentation 0 → τ →

→

→ 0 of a Leibniz algebra , the Baer invariant is called the Schur multiplier of relative to the Liezation functor or Schur Lie-multiplier. For a two-sided ideal of a Leibniz algebra , we construct a four-term exact sequence relating the Schur Lie-multipliers of and /, which is applied to study and characterize Lie-nilpotency, Lie-stem covers and Lie-capability of Leibniz algebras.

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