幂零-中心化方法的一个应用

试图丰富谱任意符号模式矩阵类.给出了一个新的含有2n个非零元的符号模式矩阵,并运用幂零-中心化方法与幂零-雅可比方法分别研究了该模式的所有母模式是谱任意的.进一步证明了该模式是极小谱任意的.最后比较了两种证明方法的联系与区别.     

Multi-graded nilpotent tuples

We discuss multi-graded nilpotent tuples of multi-graded vector spaces which are a generalization of graded nilpotent pairs. The multi-grading yields a natural notion of a shape of such tuple and our main interest is to answer the question “Is the number of multi-graded nilpotent tuples of a fixed shape, up to base change in the homogeneous components, finite?” Our methods make use of a translation to the class of so-called “Multi-staircase algebras” and we classify their representation types.     

Some remarks on Richardson orbits in complex symmetric spaces

Roger W. Richardson proved that any parabolic subgroup of a complex semisimple Lie group admits an open dense orbit in the nilradical of its corresponding parabolic subalgebra. In the case of complex symmetric spaces we show that there exist some large classes of parabolic subgroups for which the analogous statement which fails in general, is true. Our main contribution is the extension of a theorem of Peter E. Trapa (in 2005) to real semisimple exceptional Lie groups.

     

Binary Lie algebras satisfying the third Engel condition

Let Φ be a unital associative commutative ring with 1/2. The local nilpotency is proved of binary Lie Φ-algebras satisfying the third Engel condition. Moreover, it is proved that this class of algebras does not contain semiprime algebras.     

Fuzzy subgroups of nilpotent groups

In 1991, Asaad has suggested the following question: What can be said about the structure of a group G when information is known about the structure of a fuzzy subgroup A of G and vice-versa? This question has been partially investigated in Fuzzy Sets and Systems39 (1991) 323–328. The purpose of this paper is to continue more investigations for the above mentioned question.     

The Hypoellipticity for a Class of Nonhomogeneous Convolution Operator on the Nilpotent Lie Group H~n×R~k

In this paper,we use the method of representation of Lie group to study a class of nonhomoge-neous convolution operator on the nilpotent Lie group H~M×R~k,and give a criteerion of their hypoellipticity.     

非负半环上强保持幂零矩阵的线性算子

Let S be an antinegative commutative semiring without zero divisors and M_n(S)be the semiring of all n×n matrices over S.For a linear operator L on M_n(S),we say that L strongly preserves nilpotent matrices in M_n(S)if for any A∈M_n(S),A is nilpotent if and only if L(A)is nilpotent.In this paper,the linear operators that strongly preserve nilpotent matrices over S are characterized.     

On Coleman automorphisms of finite nilpotent groups by cyclic groups

Let G be a finite group and let N be a nilpotent normal subgroup of G such that G/N is cyclic. It is shown that under some conditions all Coleman automorphisms of G are inner. Interest in such automorphisms arose from the study of the normalizer problem for integral group rings.