On the Schur $\mathsf{Lie}$-multiplier and $\mathsf{Lie}$-covers of Leibniz $n$-algebras

On some properties of $\mathsf{Lie}$-centroids of Leibniz algebras

We study some properties on $\mathsf{Lie}$-centroids related to central $\mathsf{Lie}$-derivations, generalized $\mathsf{Lie}$-derivations and almost inner $\mathsf{Lie}$-derivations. We also determine the $\mathsf{Lie}$-centroid of the tensor product of a commutative associative algebra and a Leibniz algebra.

李幂零 Leibniz n-代数的 Schur 李-乘子的维数上界

Upper bounds on the dimension of the Schur $\mathsf{Lie}$-multiplier of $\mathsf{Lie}$-nilpotent Leibniz $n$-algebras

本文研究了李-丝状 Leibniz n-代数的 Schur 李-乘子维数上界，发现其与 Pascal 三角形性质相关，并改进了具有 d 维李-换位子的 m 维李-幂零 Leibniz n-代数的现有上界。

Some properties of the Schur multiplier and stem covers of Leibniz crossed modules

In this article we investigate the interplay between stem covers, the Schur multiplier of Leibniz crossed modules and the non-abelian exterior product of Leibniz algebras. In concrete, we obtain a six-term exact sequence associated to a central extension of Leibniz crossed modules, which is useful to characterize stem covers. We show the existence of stem covers and determine the structure of all stem covers of Leibniz crossed modules. Also, we give the connection between the stem cover of a Lie crossed module in the categories of Lie and Leibniz crossed modules respectively.

The c-Nilpotent Shur Lie-Multiplier of Leibniz Algebras

We introduce the notion of c-nilpotent Schur Lie-multiplier of Leibniz algebras. We obtain exact sequences and formulas of the dimensions of the underlying vector spaces relating the c-nilpotent Schur Lie-multiplier of a Leibniz algebra Q and its quotient by a two-sided ideal. These tools are used to characterize Lie-nilpotency and c-Lie-stem covers of Leibniz algebras. We prove the existence of c-Lie-stem covers for finite dimensional Leibniz algebras and the non existence of c-covering on certain Lie-nilpotent Leibniz algebras with non trivial c-nilpotent Schur Lie-multiplier, and we provide…

Lie 代数与 Leibniz 代数的 Schur 型与 Baer 型定理

Schur- and Baer-type theorems for Lie and Leibniz algebras

本文利用非 Abel 张量积和外积，将经典 Schur 与 Baer 关于换位子群有限性的定理推广到域上的有限生成 Leibniz、Lie 代数及有限呈现 Lie 代数。

The Schur Lie-Multiplier of Leibinz Algebras

For a free presentation $0 \to R \to F \to G \to 0$ of a Leibniz algebra $G$, the Baer invariant ${\cal M}^{\sf Lie}(G) = \frac{R \cap [F, F]_{Lie}}{[F, R]_{Lie}}$ 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.