算子代数上2-局部Lie三重导子的结构

设X是维数大于2的Banach空间,映射δ:B(X)→B(X)是2-局部Lie三重导子,则对所有A∈B(X)有δ(A)=[A,T]+ψ(A),这里T∈B(X),ψ是从B(X)到FI的齐次映射且满足对所有A,B∈B(X)有ψ(A+B)=ψ(A),其中B是交换子的和.     

Weak-local derivations and homomorphisms on C*-algebras

We prove that every weak-local derivation on a C*-algebra is continuous, and the same conclusion remains valid for weak*-local derivations on von Neumann algebras. We further show that weak-local derivations on C*-algebras and weak*-local derivations on von Neumann algebras are derivations. We also study the connections between bilocal derivations and bilocal*-automorphism with our notions of extreme-strong-local derivations and automorphisms.     

Local automorphisms and derivations on

The aim of this note is to give a short proof that 2-local derivations on , the matrix algebra over the complex numbers are derivations and to give a shorter proof that 2-local *-automorphisms on are *-automorphisms.

     

基本典型李超代数的2-局部超导子

设$\mathbb{F}$是特征零代数闭域, $L$是域$\mathbb{F}$上除$A(n; n)$之外的基本典型李超代数. 本文证明了$L$上2-局部超导子是超导子,并且以spl(2; 2)的一个子代数为例说明存在2局部超导子不是超导子.     

2-Local Automorphisms on Basic Classical Lie Superalgebras

Let G be a basic classical Lie superalgebra except A(n, n) and D(2, 1, α) over the complex number field C. Using existence of a non-degenerate invariant bilinear form and root space decomposition, we prove that every 2-local automorphism on G is an automorphism. Furthermore, we give an example of a 2-local automorphism which is not an automorphism on a subalgebra of Lie superalgebra spl(3, 3).     

Lie *-Nilpotence of Group Rings

Let KG be the group ring of a group G over a field K. Let * be an involution of a group G extended linearly to the group ring KG. Suppose that G is a torsion group without 2-elements and K is a field with characteristic different from 2. We prove that KG is Lie *-nilpotent if and only if KG is Lie nilpotent.     

A Note on Lie Automorphisms,Subrings, and Lie Ideals of Prime Rings

ABSTRACT

Let R be a prime ring of characteristic not 2 or 3 and L a noncentral Lie ideal of R. Suppose that σ is a Lie automorphism on L such that σ² ? 1 is noncentral on L, where 1 is the identity map, then the subring of R generated by the set {[x ^σ, x] | x ∈ L} contains a nonzero ideal of R.     

李color代数的T~*-扩张

介绍了李color代数的T*-扩张的定义,并证明李color代数的很多性质,如幂零性、可解性和可分解性,都可以提升到它的T*-扩张上.还证明在特征不等于2的代数闭域上,有限维幂零二次李color代数A等距同构于一个幂零李color代数B的T*-扩张,并且B的幂零长度不超过A的一半.此外,用上同调的方法研究了李color代数的T*-扩张的等价类.     

On CAP*-subalgebras of Lie Algebras

A subalgebra H of a Lie algebra L is said a CAP*-subalgebra if, for any non-Frattini chief factor A/B of L, we have H + A = H + B or H ∩ A = H ∩ B. In this article, using this concept, we give some characterizations of solvability and supersolvability of a finite dimensional Lie algebra.     

2-local superderivations on a superalgebra $${{\rm M}_{\rm n}({\mathbb C})}$$

The aim of this paper is to show that every 2-local superderivation on an associative superalgebra is a superderivation.      

AF C*-代数中的Lie理想

本文描述了AF C*-代数中闭Lie理想,证明了如果AF C*-代数A中的线性流形L 是A的闭Lie理想,则存在A的闭结合理想I和A的典型masa D中的闭子代数EI使得[A,I](?)L(?)I EI,并且A中每一个这种形式的闭子空间都是A的闭Lie理想.     

Power-Centralizing Automorphisms of Lie Ideals in Prime Rings

Let R be a prime ring with center Z, L a noncentral Lie ideal of R, and σ a nontrivial automorphism of R such that [u ^σ,u] ⁿ  ∈ Z for all u ∈ L. If either char(R) > n or char(R) = 0, then R satisfies s ₄, the standard identity in 4 variables.     

Automorphism Groups of Restricted Cartan-Type Lie Superalgebras

Let X denote the restricted Lie superalgebras of Cartan type W, S, H, or K over a field of characteristic p > 3, and 𝔄 the corresponding underlying superalgebra of X. Employing the invariance of the filtration of X we construct an isomorphism of Aut X to Aut(𝔄:X), the admissible automorphism group of the associative super-commutative superalgebra 𝔄. Moreover, it is proved that the group isomorphism above maps the standard normal series of Aut X to the one of Aut(𝔄:X), and also maps the homogeneous automorphism group of X to the admissible homogeneous automorphism group of 𝔄.     

Integrable cocycles and global deformations of Lie algebra of type G2 in characteristic 2

All classes of integrable cocycles in H²(L,L) are obtained for Lie algebra of type G₂ over an algebraically closed field of characteristic 2. It is proved that there exist only two orbits of classes of integrable cocycles with respect to automorphism group. The global deformation is shown to exist for any nontrivial class of integrable cocycles. These deformations are isomorphic to one of the two algebras of Cartan type, one of which being S(3:1,ω) while the other H(4:1,ω).     

Hilbert $C^*$-模算子代数上Lie三重导子的刻画

假设$\mathcal A$是一个含单位元$e$的交换$C^*$-代数, $\mathcal M$是一个满的Hilbert $\mathcal A$-模. 令End_{$\mathcal A$}($\mathcal M$)表示$\mathcal M$上的全体有界$\mathcal A$线性算子构成的代数, $\mathcal M''$M表示$\mathcal M$到$\mathcal A$的全体有界$\mathcal A$线性映射构成的集合. 在本文中, 我们证明了如果存在$\mathcal M$中元素$x_0$和$\mathcal M''$中的元素$f_0$满足$f_0(x_0)=e$, 那么End_{$\mathcal A$}($\mathcal M$)上的$\mathcal A$-线性Lie三重导子都是标准的.     

Automorphisms of infinite dimensional Lie algebras of Cartan type

In this paper it is proved that any automorphism of an infinite dimensional Lie algebra of Cartan type over an algebraically closed field of characteristicp>2 can be induced from an automorphism of the associated divided power algebra.