The Schur Lie-multiplier of Leibniz algebras

DOI10.2989/16073606.2017.1417335zbMATH Open1464.17005arXiv1703.07148OpenAlexW2962835780WikidataQ123138217 ScholiaQ123138217MaRDI QIDQ4562706

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Publication date: 18 December 2018

Published in: (Search for Journal in Brave)

Abstract: For a free presentation $0oRoFoGo0$ of a Leibniz algebra $G$, the Baer invariant ${calM}^{sfLie}(G)=fracRcap[F,F{]}_{Lie}[F,R{]}_{Lie}$ 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.

Full work available at URL: https://arxiv.org/abs/1703.07148

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