严格上三角矩阵李代数上的积零导子

设$F$ 为域, $n\geq 3$, $\bf{N}$$(n,\mathbb{F})$ 为域$\mathbb{F}$ 上所有$n\times n$ 阶严格上三角矩阵构成的严格上三角矩阵李代数, 其李运算为$[x,y]=xy-yx$. $\bf{N}$$(n, \mathbb{F})$ 上一线性映射$\varphi$ 称为积零导子,如果由$[x,y]=0, x,y\in \bf{N}$$(n,\mathbb{F})$,总可推出 $[\varphi(x), y]+[x,\varphi(y)]=0$. 本文证明 $\bf{N}$$(n,\mathbb{F})$上一线性映射 $\varphi$ 为积零导子当且仅当 $\varphi$ 为$\bf{N}$$(n,\mathbb{F})$ 上内导子, 对角线导子, 极端导子, 中心导子和标量乘法的和.     

4维幂零李代数的导子与triple导子

利用导子和triple导子的定义,刻画了特征不等于2的代数闭域上4维幂零李代数的导子和triple导子.     

TUHF代数上的Lie导子

证明了TUHF代数丁上的Lie导子L形如D l．其中D是T上的结合导子，l是从T到它的中心Z上的线性映射且零化T中的括积．     

三角代数上的广义Jordan导子

主要研究了三角代数上的广义Jordan导子．利用三角代数上广义Jordan导子和广义内导子的联系．证明了作用在一个含单位元的可交换环上的三角代数到其自身上的环线性广义Jordan导子是一个广义导子．     

Filiform李超代数Ln,m的导子和保积Hom-结构

将李超代数的导子和Hom-结构表示为矩阵,通过计算,具体刻画了特征零的代数闭域上Filiform李超代数Ln,m 的导子代数和保积Hom-结构。     

三角代数上的Jordan双导子（英文）

设T是定义在交换环上R的三角代数,φ:T×T→T是定义在T上的任意Jordan双导子.受[Comm.Algebra,2017,45(4):1741-1756]和[Linear Algebra Appl.,2009,431(9):1587-1602]研究的启发,本文致力研究φ的结构形式.我们指出在适当条件下Jordan双导子φ可以分解成内双导子和extremal双导子之和,推广了本方向现有成果.本文结果可直接应用于分块上三角矩阵代数和Hilbert空间定义的套代数.     

可换环上严格上三角矩阵李代数的BZ导子

本文研究了严格上三角矩阵李代数的BZ导子.利用BZ导子在其基上的作用,获得了严格上三角矩阵李代数的任意一个BZ导子的具体形式.对导子的概念进行了推广.     

三角代数上的Jordan零点ξ-Lie可导映射

给出了三角代数上Jordan零点ξ-Lie可导映射的结构.作为应用,得到了套代数上Jordan零点ξ-Lie可导映射的具体形式.     

一类广义W型李超代数

构造了一类有限维广义Caxtan型模李超代数W,并证明了它是李超代数W(n)的一个扩张,进而决定了它的导子超代数.     

特征幂零n-Lie代数

研究了一类特殊的幂零n-Lie代数,其所有导子都是幂零的,称其为特征幂零n-Lie代数.本文主要是得到了一般的n-Lie代数是特征幂零n-Lie代数的一些充要条件.     

零积决定的矩阵代数

本文研究了零积决定的矩阵代数A=Mn(B)的条件及分类问题.利用基矩阵及巧妙对线性映射T进行构造和扩充,用初等矩阵的方法.获得了较为简单直接的新的证明(对于文献[1]中一系列的问题),并还对其遗留的问题n=2的情形给予一并解决,推广了文献[1]中的结论.     

Generalized skew derivations on triangular algebras determined by action on zero products

For a triangular algebra 𝒜 and an automorphism σ of 𝒜, we describe linear maps F,G:𝒜→𝒜 satisfying F(x)y+σ(x)G(y) = 0 whenever x,y∈𝒜 are such that xy = 0. In particular, when 𝒜 is a zero product determined triangular algebra, maps F and G satisfying the above condition are generalized skew derivations of the form F(x) = F(1)x+D(x) and G(x) = σ(x)G(1)+D(x) for all x∈𝒜, where D:𝒜→𝒜 is a skew derivation. When 𝒜 is not zero product determined, we show that there are also nonstandard solutions for maps F and G.     

Jordan higher derivable maps on triangular algebras by commutative zero products

In this paper, the structure of Jordan higher derivable maps on triangular algebras by commutative zero products is given. As an application, the form of Jordan higher derivable maps of nest algebras by commutative zero products is obtained.     

Zero Divisors in Amalgamated Free Products of Lie Algebras

We introduce the notion of domain for Lie algebras, discuss when the free amalgamated Lie product of two domains is a domain again, classify commuting elements in the free amalgamated product of two Lie algebras and describe the center of this product.     

Zero product preserving maps on Banach algebras of Lipschitz functions

Let (K,d) be a non-empty, compact metric space and α∈]0,1[. Let A be either lipα(K) or Lipα(K) and let B be a commutative unital Banach algebra. We show that every continuous linear map T:A→B with the property that T(f)T(g)=0 whenever f,g∈A are such that fg=0 is of the form T=wΦ for some invertible element w in B and some continuous epimorphism Φ:A→B.     

Wild radical square zero algebras

It is shown that a radical square zero algebra is wild, if and only if it is of Corner’s type, and it is strictly wild if and only if it is Endo-wild. This gives a negative answer to a problem posed by Simson.     

Zeroes of slice monogenic functions

In this article, we study the structure of zeroes of power series with Clifford algebra‐valued coefficients. Especially, if it has paravector‐valued coefficients, we obtain some sufficient and necessary conditions of power series that have zeroes, as well as a method to compute the zeroes if exist. Copyright 2011 John Wiley & Sons, Ltd.     

Hom-Hopf 代数上的交叉积

在Hom-Hopf代数上,定义了Hom-交叉积的概念．并且,得到了它的两种特殊形式：Hom-smash积和Hom-扭积．并且,给出了Hom-扭积是Hom—Hopf代数的充要条件．     

Class Partition Algebras as Centralizer Algebras of Wreath Products

In this article, we study an important subalgebra of the tensor product partition algebra P _k (x)? P _k (y), denoted by P _k (x, y) and called “Class Partition Algebra.” We show that the algebra P _k (n, m) is the centralizer algebra of the wreath product S _m ? S _n . Furthermore, the algebra P _k (x, y) and the tensor product partition algebra P _k (x)? P _k (y) are subalgebras of the G-colored partition algebra P _k (x;G) and G-vertex colored partition algebra P _k (x, G) respectively, for every group G with |G|=y ≥ 2k.