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Start Over Creator Wang, Dengyin

1. Non-linear maps preserving ideals on a parabolic subalgebra of a simple algebra

Creator:
Wang, Dengyin, Pan, Haishan, and Wang, Xuansheng
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
simple associative $F$-algebra, ideals, and maps preserving ideals
Language:
English
Description:
Let $\Cal P$ be an arbitrary parabolic subalgebra of a simple associative $F$-algebra. The ideals of $\Cal P$ are determined completely; Each ideal of $\Cal P$ is shown to be generated by one element; Every non-linear invertible map on $\Cal P$ that preserves ideals is described in an explicit formula.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The group of commutativity preserving maps on strictly upper triangular matrices

Creator:
Wang, Dengyin, Zhu, Min, and Rou, Jianling
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
commutativity preserving map, automorphism, and commutative ring
Language:
English
Description:
Let $\mathcal {N}=N_n(R)$ be the algebra of all $n\times n$ strictly upper triangular matrices over a unital commutative ring $R$. A map $\varphi $ on $\mathcal {N}$ is called preserving commutativity in both directions if $xy=yx\Leftrightarrow \varphi (x)\varphi (y)=\varphi (y)\varphi (x)$. In this paper, we prove that each invertible linear map on $\mathcal {N}$ preserving commutativity in both directions is exactly a quasi-automorphism of $\mathcal {N}$, and a quasi-automorphism of $\mathcal {N}$ can be decomposed into the product of several standard maps, which extains the main result of Y. Cao, Z. Chen and C. Huang (2002) from fields to rings.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. Triple automorphisms of simple Lie algebras

Creator:
Wang, Dengyin and Yu, Xiaoxiang
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
simple Lie algebras, parabolic subalgebras, and triple automorphisms of Lie algebras
Language:
English
Description:
An invertible linear map $\varphi $ on a Lie algebra $L$ is called a triple automorphism of it if $\varphi ([x,[y,z]])=[\varphi (x),[ \varphi (y),\varphi (z)]]$ for $\forall x, y, z\in L$. Let $\frak {g}$ be a finite-dimensional simple Lie algebra of rank $l$ defined over an algebraically closed field $F$ of characteristic zero, $\mathfrak {p}$ an arbitrary parabolic subalgebra of $\mathfrak {g}$. It is shown in this paper that an invertible linear map $\varphi $ on $\mathfrak {p}$ is a triple automorphism if and only if either $\varphi $ itself is an automorphism of $\mathfrak {p}$ or it is the composition of an automorphism of $\mathfrak {p}$ and an extremal map of order $2$.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public