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Liangyun Chen

Publications and source records attributed to Liangyun Chen.

At least 55 records · Page 3Linked to original sources
arXiv2019

Local superderivations on Cartan type Lie superalgebras

In this paper, we characterize the local superderivations on Cartan type Lie superalgebras over the complex field $\mathbb{C}$. Furthermore, we prove that every local superderivations on Cartan type simple Lie superalgebras is a superderivations. As an application, using the results on local superderivations we characterize the $2$-local superderivations on Cartan type Lie superalgebras. We prove that every $2$-local superderivations on Cartan type Lie superalgebras is a superderivations.

math.RA↗
arXiv2019

Quasi-derivations of Lie-Yamaguti algebras

The concept of derivation for Lie-Yamaguti algebras is generalized in this paper. A quasi-derivation of an LY-algebra is embedded as derivation in a larger LY-algebra. The relationship between quasi-derivations and robustness of Lie-Yamaguti algebras has been studied.

math.RA↗
arXiv2018

Super-biderivations of Cartan type Lie superalgebras

In this paper, we characterize the super-biderivations of Cartan type Lie superalgebras over the complex field $\mathbb{C}$. Furthermore, we prove that all super-biderivations of Cartan type simple Lie superalgebras are inner super-biderivations.

math.RA↗
arXiv2018

On universal $α$-central extensions of Hom-preLie algebras

We introduce the notion of Hom-co-represention and low-dimensional chain complex. We study universal central extensions of Hom-preLie algebras and generlize some classical results. As the same time, we introduce $α$-central extensions, universal $α$-central extensions and $α$-perfect Hom-preLie algebras. We construct universal ($α$)-central extensions of Hom-preLie algebras.

math.RA↗
arXiv2017

The explicit Plancherel formula on the line budle of ${\rm SL}(n+1, {\mathbb R})/{\rm S}({\rm GL}(1, {\mathbb R})\times {\rm GL}(n, {\mathbb R}))$

The purpose of this paper is to study the Plancherel formula for the spaces of $L^2$-sections of the line bundles over the pseudo-Riemannian space $G/H$, where $G={\rm SL}(n+1, {\mathbb R})$ and $H={\rm S}({\rm GL}(1, {\mathbb R})\times {\rm GL}(n, {\mathbb R}))$. The formula is given in an explicit form by means of spherical distributions associated with the character $χ_{_λ}$ of the subgroup $H$.

math.DG↗
arXiv2017

Deformations and generalized derivations of Hom-Lie conformal algebras

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce $α^k$-derivations of multiplicative Hom-Lie conformal algebras and study their properties.

math.RA↗
arXiv2016

Deformations and generalized derivations of Lie conformal superalgebras

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and its conformal module, and study derivations of this semidirect product. Secondly, we develop cohomology theory of Lie conformal superalgebras and discuss some applications to the study of deformations of Lie conformal superalgebras. Finally, we introduce generalized derivations of Lie conformal superalgebras and study their properties.

math.RA↗
arXiv2016

Triple Derivations and Triple Homomorphisms of Perfect Lie Superalgebras

In this paper, we study triple derivations and triple homomorphisms of perfect Lie superalgebras over a commutative ring $R$. It is proved that, if the base ring contains $\frac{1}{2}$, $L$ is a perfect Lie superalgebra with zero center, then every triple derivation of $L$ is a derivation, and every triple derivation of the derivation algebra $ Der (L)$ is an inner derivation. Let $L,~L^{'}$ be Lie superalgebras over a commutative ring $R$, the notion of triple homomorphism from $L$ to $L^{'}$ is introduced. We proved that, under certain assumptions, homomorphisms, anti-homomorphisms, and sums of homomorphisms and anti-homomorphisms are all triple homomorphisms.

math.RA↗
arXiv2016

Derivations from the even parts into the odd parts for Hamiltonian superalgebras

Let $W_{\overline{1}}$ and $H_{\overline{0}}$ denote the odd parts of the general Witt modular Lie superalgebra $W$ and the even parts of the Hamiltonian Lie superalgebra $H$ over a field of characteristic $p>3$, respectively. We give a torus of $H_{\overline{0}}$ and the weight space decomposition of the special subalgebra of $W_{\overline{1}}$ with respect to the torus. By means of the derivations of the weight 0 and three series of outer derivations from $H_{\overline{0}}$ into $W_{\overline{1}}$, the derivations from the even parts of Hamiltonian superalgebra to the odd parts of Witt superalgebra are determined.

math.RA↗
arXiv2016

3-ary Hom-Lie superalgebras induced Hom-Lie superalgebras

The purpose of this paper is to study the relationships between a Hom-Lie superalgebra and its induced 3-ary-Hom-Lie superalgebra. We provide an overview of the theory and explore the structure properties such as ideals, center, derived series, solvability, nilpotency, central extensions, and the cohomology.

math.RA↗
arXiv2016

On the structure of graded Leibniz triple systems

We study the structure of a Leibniz triple system $\mathcal{E}$ graded by an arbitrary abelian group $G$ which is considered of arbitrary dimension and over an arbitrary base field $\mathbb{K}$. We show that $\mathcal{E}$ is of the form $\mathcal{E}=U+\sum_{[j]\in \sum^{1}/\sim} I_{[j]}$ with $U$ a linear subspace of the 1-homogeneous component $\mathcal{E}_{1}$ and any ideal $I_{[j]}$ of $\mathcal{E}$, satisfying $\{I_{[j]},\mathcal{E},I_{[k]}\} =\{I_{[j]},I_{[k]},\mathcal{E}\}=\{\mathcal{E},I_{[j]},I_{[k]}\}=0$ if $[j]\neq [k]$, where the relation $\sim$ in $\sum^{1}=\{g \in G \setminus \{1\} : L_{g}\neq 0\}$, defined by $g \sim h$ if and only if $g$ is connected to $h$.

math.RA↗
arXiv2015

Some structure theories of Leibniz triple systems

In this paper, we investigate the Leibniz triple system $T$ and its universal Leibniz envelope $U(T)$. The involutive automorphism of $U(T)$ determining $T$ is introduced, which gives a characterization of the $\Z_2$-grading of $U(T)$. We give the relationship between the solvable radical $R(T)$ of $T$ and $Rad(U(T))$, the solvable radical of $U(T)$. Further, Levi's theorem for Leibniz triple systems is obtained. Moreover, the relationship between the nilpotent radical of $T$ and that of $U(T)$ is studied. Finally, we introduce the notion of representations of a Leibniz triple system.

math.RA↗
arXiv2015

Restricted hom-Lie algebras

The paper studies the structure of restricted hom-Lie algebras. More specifically speaking, we first give the equivalent definition of restricted hom-Lie algebras. Second, we obtain some properties of $p$-mappings and restrictable hom-Lie algebras. Finally, the cohomology of restricted hom-Lie algebras is researched.

math.RA↗
arXiv2015

Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras

In this paper, we introduce the concepts of Rota-Baxter operators and differential operators with weights on a multiplicative $n$-ary Hom-algebra. We then focus on Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras and show that they can be derived from Rota-Baxter Hom-Lie algebras, Hom-preLie algebras and Rota-Baxter commutative Hom-associative algebras. We also explore the connections between these Rota-Baxter multiplicative 3-ary Hom-Nambu-Lie algebras.

math-ph↗
arXiv2015

On split regular Hom-Lie color algebras

We introduce the class of split regular Hom-Lie color algebras as the natural generalization of split Lie color algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Lie color algebra $L$ is of the form $L = U + \sum\limits_{[j] \in Λ/\sim}I_{[j]}$ with $U$ a subspace of the abelian graded subalgebra $H$ and any $I_{[j]}$, a well described ideal of $L$, satisfying $[I_{[j]}, I_{[k]}] = 0$ if $[j]\neq [k]$. Under certain conditions, in the case of $L$ being of maximal length, the simplicity of the algebra is characterized.

math.RA↗
arXiv2015

On split Regular Hom-Leibniz algebras

We introduce the class of split regular Hom-Leibniz algebras as the natural generalization of split Leibniz algebras and split regular Hom-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular Hom-Leibniz algebra $L$ is of the form $L = U + \sum\limits_{[j] \in Λ/\sim}I_{[j]}$ with $U$ a subspace of the abelian subalgebra $H$ and any $I_{[j]}$, a well described ideal of $L$, satisfying $[I_{[j]}, I_{[k]}] = 0$ if $[j]\neq [k]$. Under certain conditions, in the case of $L$ being of maximal length, the simplicity of the algebra is characterized.

math.RA↗
arXiv2015

$n$-ary Hom-Nambu algebras

In this paper, we define $ω$-derivations, and study some properties of $ω$-derivations, with its properties we can structure a new $n$-ary Hom-Nambu algebra from an $n$-ary Hom-Nambu algebra. In addition, we also give derivations and representations of $n$-ary Hom-Nambu algebras.

math.RA↗