Another super-identity equivalent to the Hom-Malcev super-identity

Malcev双代数

Malcev dialgebras

我们应用Kolesnikov的算法来获得各种非结合代数定义的右反交换性和一个“非交换”版本的Malcev身份。利用计算线性代数证明了这些恒等式等价于每一个交错双代数中双交换子满足的次数<= 4的恒等式。我们扩展这些计算表明，任何特殊的身份Malcev双代数必须有度至少为7。最后，我们引入了一个三线性运算，它使任何Malcev双代数成为一个Leibniz三元系。

Hom-Jordan-Malcev-Poisson algebras

The purpose of this paper is to provide and study a Hom-type generalization of Jordan-Malcev-Poisson algebras, called Hom-Jordan-Malcev-Poisson algebras. We show that they are closed under twisting by suitable self-maps and give a characterization of admissible Hom-Jordan-Malcev-Poisson algebras. In addition, we introduce the notion of pseudo-Euclidian Hom-Jordan-Malcev-Poisson algebras and describe its $T^*$-extension. Finally, we generalize the notion of Lie-Jordan-Poisson triple system to the Hom setting and establish its relationships with Hom-Jordan-Malcev-Poisson algebras.

Kupershmidt operators on Hom-Malcev algebras and their deformation

The main feature of Hom-algebras is that the identities defining the structures are twisted by linear maps. The purpose of this paper is to introduce and study a Hom-type generalization of pre-Malcev algebras, called Hom-pre-Malcev algebras. We also introduce the notion of Kupershmidt operators of Hom-Malcev and Hom-pre-Malcev algebras and show the connections between Hom-Malcev and Hom-pre-Malcev algebras using Kupershmidt operators. Hom-pre-Malcev algebras generalize Hom-pre-Lie algebras to the Hom-alternative setting and fit into a bigger framework with a close relationship with Hom-pre-alt…

Dendrification of Hom-Malcev algebras

The main goal of this work is to introduce the notion of Hom-M-dendriform algebras which are the dendriform version of Hom-Malcev algebras. In fact they are the algebraic structures behind the $\mathcal{O}$-operator of Hom-pre-Malcev algebras. They also fit into a bigger framework as Hom-Malcev algebraic analogues of Hom-L-dendriform algebras. Furthermore, we show a connections between Hom-M-Dendriform algebras and Hom-alternative quadri-algebras.

一类Hom-Sabinin代数及其相关代数子类

Variety of Hom-Sabinin algebras and related algebra subclasses

本文研究了Hom-type的Sabinin代数。证明了Lie，Malcev，Bol等Hom-型代数自然是Hom-型Sabinin代数.为此，我们提供了一个通用的关键建设，建立了一些类的Hom-algebras和普通代数的身份之间的关系。此外，我们还讨论了与泛包络Hom-代数有关的Hom-双代数的一个新概念。提供了基于本原元的研究。

右Hom-交错代数中的Mikheev恒等式

The Mikheev identity in right Hom-alternative algebras

证明了在每个乘法右Hom-交错代数中，Mikheev恒等式的一个Hom型推广成立.然后，我们得到了具有单射扭映射且不含Hom-幂零元和左零因子的乘法右Hom-交错代数必是Hom-交错代数的结论.

Hom-Leibniz代数的一些特征

Some characterizations of Hom-Leibniz algebras

得到了Hom-Leibniz代数的一些基本性质，这些性质是Leibniz代数的一些著名性质的Hom-analogue。考虑与给定的Hom-Leibniz代数相关联的Hom-Akivis代数，观察到Hom-Akivis恒等式导致Hom-Leibniz代数的一个附加性质，进而给出Hom-Leibniz代数的Hom-Lie容许性的一个充要条件.并给出了Hom-Leibniz代数的Hom-power结合性的一个充要条件。

On Hom-Leibniz and Hom-Lie-Yamaguti Superalgebras

In this paper some characterizations of Hom-Leibniz superalgebras are given and some of their basic properties are found. These properties can be seen as a generalization of corresponding well-known properties of Hom-Leibniz algebras. Considering the Hom-Akivis superalgebra associated to a given Hom-Leibniz superalgebra, it is observed that the Hom-super Akivis identity leads to an additional property of Hom-Leibniz superalgebras, which in turn gives a necessary and sufficient condition for Hom-super Lie admissibility of Hom-Leibniz superalgebras. We show also that every (left) Hom-Leibniz sup…

Hom-Lie超代数与Hom-Lie容许超代数

Hom-Lie Superalgebras and Hom-Lie admissible Superalgebras

本文研究了Hom-Lie超代数，即具有一个括号的超空间，其超Jacobi恒等式被同态扭曲。这类代数是Larsson和Silvestrov引入的$Γ$ -分次拟李代数的一个特例。本文刻画了Hom-Lie可容许超代数，并给出了一个构造定理，由此得到了一类单参数Hom-Lie超代数族，该超代数族变形正交辛李超代数.此外，我们证明了一个$\mathbb{Z}_2$ -分级版本的Hartwig-Larsson-Silvestrov定理，这使我们的一个q-变形的Witt超代数的建设。

$\mathfrak{sl}_2$的微分变形与扭曲的雅可比恒等式

Infinitesimal deformations of $\mathfrak{sl}_2$ with a twisted Jacobi identity

研究$\mathfrak{sl}_2$的微分变形，证明在满足特定条件时，变形后括号满足普通雅可比恒等式，解决Makhlouf和Silvestrov于2010年的猜想。