无限秩典型根系的自同构

所谓一个无限秩典型根系△是指型Ａ∞,Ａ＋∞,Ｂ∞,Ｃ∞或Ｄ∞的无限秩根系的一种．对任一非 负整数ｌ,△包含一个有限根系△ｌ,使得△０ △１ …且△＝Ｕｌ＝０∞△ｌ．本文的工作是求出△的 保持每一△ｎｉ的所有自同构,其中ｎｉ属于集合｛ｎｉ）,集合｛ｎｉ｜ｉ＝１,２,…｝是任一给定的非负整 数序列且 ｎ１＜ｎ２＜…．这是有限根系的自同构群的推广．     

无限秩仿射李代数的Cartan子代数的共轭性

本文给出了无限秩仿射李代数的某种类型的Cartan子代数的定义,并证明了这种Cartan子代数在无限秩仿射李代数的某种类型的自同构下的共轭性.     

无限秩仿射李代数的cartan子代数的共轭性

本文给出了无限秩仿射李代数的某种类型的Cartan子代数的定义,并证明了这种Cartan子代数在无限秩仿射李代数的某种类型的自同构下的共轭性.     

整环上二阶线性李代数的自同构

设Ｒ是有１的交换环，２是Ｒ的单位．本文决定了Ｒ上李代数ｓｌ２（Ｒ）的理想．进而，若Ｒ是整环，本文决定了ｓｌ２（Ｒ）与ｇｌ２（Ｒ）的自同构形式．     

具有交换幂零根基的完备李代数的自同构群

给出了复数域上具有交换幂零根基的完备李代数的自同构群．     

Cartan型李代数的自同构群

本文证明了素特征域 Ｆ上广义 Ｃａｒｔａｎ型李代数的自同构群都是 ＡｕｔＷ（ｍ,ｎ）的子群．文中对于除幂代数相应的可容许自同构给出了刻划,从而对广义 Ｃａｒｔａｎ型李代数的自同构给出了刻划     

一类量子环面李代数的自同构群

=C_q[x_1~(±1),x_2~(±1)]为复数域上的非交换环面结合代数,A=\C,Der为的导子李代数．本文研究李代数L_q=DerA的自同构群Aut L_q．     

李群的解析对合自同构对的分类

本文给出复单李代数的对合自同构对的分类,并利用它研究单连通,单李群的解析对合自同构对的分类.     

李群的解析对合自同构对的分类

本文给出复单李代数的对合自同构对的分类,并利用它研究单连通,单李群的解析对合自同构对的分类.     

量子环面的一个收缩李代数的自同构群

首先证明文[漳州师范学院学报(自然科学版),2012,25(2):9-17]中研究的李代数L与文[J.Lie Theory,2006,16(1):139-153]中所研究的李代数L不同构,接着确定了L的自同构群.     

States of Infinite Equilibrium Classical Systems

We construct a measure that corresponds to the correlation functions of equilibrium states of infinite systems of classical statistical mechanics. The correlation functions satisfy the Bogolyubov compatibility conditions. We also construct measures that correspond to the correlation functions of nonequilibrium states of infinite systems for the Boltzmann hierarchy and the Bogolyubov–Strel'tsova diffusion hierarchy.     

On the Spectrum of Cartesian Powers of Classical Automorphisms

We prove the following statement: the set of all essential spectral multiplicities of (n times) is on for Chacon transformations T, or, equivalently, the operator T(ⁿ) has a simple spectrum on the subspace C _Sim of all functions that are invariant with respect to permutations of the coordinates. As an immediate consequence of this fact, we have the disjointness of all convolution powers of the spectral measure for Chacon transformations. If n=2, then T× T has a homogeneous spectrum of multiplicity 2 on , i.e., this is a solution of Rokhlin's problem for Chacon transformations. Similar statements are considered for other classical automorphisms.     

Classical and Exceptional Root Systems and Quantizations

We present a method for quantizing semisimple Lie algebras. In Huru (Russ. Math. [2007]) we defined quantizations of the braided Lie algebra structure on a finite dimensional graded vector space V by quantizations of braided derivations on the exterior algebra of V ^* . We find quantizations of semisimple Lie algebras in this setting using the grading by their roots and shall go through all root systems, classical and exceptional.      

Classical Integrable Systems and Automorphisms of Representations of gl(2)

Outer automorphisms of infinite-dimensional representations of sl(2)algebra are applied to produce some classical integrable systems with continuous and discrete time. The associated Lax pairs and r-matrix algebras are constructed. Bibliography: 14 titles.     

On Infinite Disjoint Congruence Covering Systems

In this paper we show that for any α∈(0,l] there exists an infinite disjoint covering system {a1(modni)}i=1∞ such that     

典型根系中不可约子根系的数目

Let Ф be an irreducible root system of classical type. In this short note, we study the irreducible subsystems of Ф and compute the number of irreducible subsystems of any rank k in Ф.