Existentially closed Leibniz algebras and an embedding theorem

Hom-Lie 代数上的嵌入张量

Embedding tensors on Hom-Lie algebras

本文在 Hom-Lie 代数上引入了嵌入张量，构造了刻画它的分次 Lie 代数与控制 $L_\infty$-代数，定义了相关上同调与 Hom-Lie-Leibniz 三元组，并探讨了同伦嵌入张量与 $HLeib_\infty$-代数的关系。

Nonabelian embedding tensors

In this paper, first we introduce the notion of a nonabelian embedding tensor, which is a nonabelian generalization of an embedding tensor. Then we introduce the notion of a Leibniz-Lie algebra, which is the underlying algebraic structure of a nonabelian embedding tensor, and can also be viewed as a nonabelian generalization of a Leibniz algebra. Next using the derived bracket, we construct a differential graded Lie algebra, whose Maurer-Cartan elements are exactly nonabelian embedding tensors. Consequently, we obtain the differential graded Lie algebra that governs deformations of a nonabelia…

3-Hom-Lie 代数上的嵌入张量

Embedding tensors on 3-Hom-Lie algebras

本文引入了3-Hom-Lie代数上的嵌入张量概念并诱导出3-Hom-Leibniz代数，定义了其上同调理论，并证明了等价线性形变的无穷小量属于第一上同调群中的同一上同调类。

原斜纹莱布尼茨代数中的形变映射

Deformation maps in proto-twilled Leibniz algebras

该研究在原斜纹莱布尼茨代数中引入形变映射以统一研究莱布尼茨代数上各类算子的上同调，构造了对应弯曲$L_\infty$-代数并给出相关算子的Maurer-Cartan刻画，还构建了控制算子及代数与算子同时形变的两个主控$L_\infty$-代数。

3-Lie代数上嵌入张量的形变与上同调

Deformations and cohomologies of embedding tensors on 3-Lie algebras

本文引入了3-Lie代数上的嵌入张量概念，构造了控制其形变的$L_{\infty}$-algebra并定义了上同调理论，揭示了形式形变等价性与延拓性由第二和第三上同调群决定。

The Tits--Kantor--Koecher construction for Jordan dialgebras

We study a noncommutative generalization of Jordan algebras called Jordan dialgebras. These are algebras that satisfy the identities $[x_1 x_2]x_3= 0$, $(x_1^2,x_2,x_3)=2(x_1,x_2,x_1x_3)$, $x_1(x_1^2 x_2)=x_1^2(x_1 x_2)$; they are related with Jordan algebras in the same way as Leibniz algebras are related to Lie algebras. We present an analogue of the Tits---Kantor---Koecher construction for Jordan dialgebras that provides an embedding of such an algebra into Leibniz algebra.

Simplicity in the Faulkner construction

We revisit the Faulkner construction of metric 3-Leibniz algebras admitting an embedding Lie (super)algebra. In the case of positive-definite signature, we relate the various notions of simplicity: of the 3-algebra, of the representation and of the embedding Lie (super)algebra. This reduces their classification to the extant classifications of simple Lie (super)algebras.

从嵌入张量构造分层李超代数

Graded Lie superalgebras from embedding tensors

本文通过嵌入张量构造分层李超代数，并揭示其与李代数模之间的关系。

一个普遍的卡卢日宁--克拉斯纳嵌入定理

A universal Kaluzhnin--Krasner embedding theorem

本文研究卡卢日宁--克拉斯纳普遍嵌入定理向其他代数结构推广的可行性，通过揭示群、李代数和余交换霍普夫代数三种已知情形的统一性，给出适配的充要条件，并证明在无限域上非结合代数中仅李代数容许该定理，而交叉模可得到相应版本。

$D$-bialgebras, dendrification和嵌入到几乎Poisson代数的AWB中

$D$-bialgebras, dendrification and embeddings into AWB of almost Poisson algebras

本文引入了几乎Poisson Drinfel'd bialgebras（$D$-bialgebras）并建立了匹配对、Manin三元组与该结构的等价性，同时定义了新的代数结构，并展示了如何通过平均算子将几乎Poisson代数嵌入到AWB中。