一些(双)代数的不可约表示

本文完全刻画了下列代数k,k,k(x,Y,Z|ZX-qXZ=1-θY2,ZY=qYZ,YX= qXY>和M(p,q)=k的不可约表示．     

量子代数Uq（C_2）的有限维不可约表示

本文分析了量子代数Ｕｑ（Ｃａ）生成元的对易关系，构造了的秩张量，利用量子代数的张性性质，方便地求出了Ｕｑ（Ｃａ）的有限维不可约表示，部分低维不可的表示被列于表中．     

非交换群上一类代数的不可约表示

在一类无限维非交换Hopf代数上,借助其Hopf理想,构造出商Hopf代数,讨论了此商代数上的有限维不可约模,得出此非平凡不可约模的维数一定是2.     

一类超W-代数权空间维数有限的不可约模

本文研究了一类超W-代数上某一权空间维数有限的不可约权模,证明了该权模必是Harish-Chandra模.     

算子强不可约的充要条件

本文证明了Cowen-Douglas 算子是强不可约的充要条件,是它的换位代数模去其Jacobson 根同构于$H^{\infty}(D)$中的一个闭子代数,这里$D$表示开单位圆盘, $H^{\infty}(D)$表示$D$上的有界解析函数的全体.     

良序套张量积的代数中的强不可约算子

设Ｈ为复的可分无限维Ｈｉｌｂｅｒｔ空间，称有界线性算子Ｔ为强不可约的，如果与Ｔ可交换的幂等算子只有０和Ｉ．王宗尧、蒋春澜、纪有清等人证明了在任何一个套的套代数中都存在大量的强不可约算子，并且找到了它们的酉轨道闭包．本文考虑有限个套的张量积的代数中强不可约算子的存在性问题。证明了：对复平面上任何一个连通完备集σ、总存在一个对角算子Ｎ和它的一个范数可以任意小的紧摄动Ｔ＝Ｘ＋Ｋ，使得Ｔ是一个强不可约算子、Ｔ在有限个良序套的张量积的代数中，并且σ（Ｔ）＝σｌｒｅ（Ｔ）＝σ（Ｎ）＝σｌｒｅ（Ｎ）＝σ进一步，文章还对具有单点谱的算子和良序套与正交补为良序套的张量积的代数进行了讨论，得到了一些结果．     

幂零算子相似于不可约算子

给出幂零算子相似于不可约算子的充要条件,并且对幂零算子证明了Herrero猜想.     

Irreducible representations over the diamond Lie algebra

In this paper, we use Block’s results to classify irreducible modules over the diamond Lie algebra 𝔇. As a corollary, we also give a classification of irreducible modules over the Euclidean algebra 𝔢(2).     

系数在基本Harish—Chandra模中的Virasoro代数的上同调群

设ｇ为特征为０的二次闭域上的Ｖｉｒａｓｏｒｏ代数。本文决定了Ｈ＾１（ｇ，Ｍ（４，１）），Ｈ＾２（ｇ，Ｍ（４，２））及Ｈ＾２（ｇ，ＭＬ）的结构，其中Ｍ（４，１），Ｍ（４，２）为两类基本Ｈａｒｉｓｈ－Ｃｈａｎｄｒａ模，ＭＬ为无常数项单变量Ｌａｕｒｅｎｔ多项式。     

Classification of Irreducible Weight Modules with a Finite-dimensional Weight Space over Twisted Heisenberg-Virasoro Algebra

We show that the support of an irreducible weight module over the twisted Heisenberg-Virasoro algebra, which has an infinite-dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the twisted Heisenber-Virasoro algebra, having a nontrivial finite-dimensional weight space, is a Harish-Chandra module （and hence is either an irreducible highest or lowest weight module or an irreducible module from the intermediate series）.     

Semisimple Lie Algebras of Differential Operators

Starting from the commutation relations in a complex semisimple Lie algebra , one may obtain a space of vector fields on Euclidean space such that and are isomorphic when is equipped with the usual Lie bracket between vector fields and the isotropy subalgebra of is a Borel subalgebra . Furthermore, one may adjoin to the vector fields in multiplication operators to obtain an -parameter family of distinct presentations of as spaces of differential operators, where is the dual of a Cartan subalgebra. Some of these presentations will preserve a space of polynomials on Euclidean space, and, in fact, all the finite-dimensional representations of can be presented in this way. All of this is carried out explicitly for arbitrary . In doing so, one discovers there is a Lie group of diffeomorphisms of the unipotent subgroup N complementary to B which acts on these presentations and preserves a certain notion of weight.     

曲线上微分算子环及其上的模

我们首先讨论了解析不可约曲线Ｘ／ｋ上微分算子环的右模Ｄ（（ｘ），Ｉ）的性质及应用，然后讨论曲线上微分算子环的有限维向量空间模和ｈｏｌｏｎｏｍｉｃ模．     

A Note on the Subdirectly Irreducible ckham Algebras

ＡＮｏｔｅｏｎｔｈｅＳｕｂｄｉｒｅｃｔｌｙＩｒｒｅｄｕｃｉｂｌｅｃｋｈａｍＡｌｇｅｂｒａｓ￥ＦａｎｇＪｉｅ（Ｄｅｐａｒｔｍｅｎｔｏｆｍａｔｈｅｍａｔｉｃｓ，ＺｈｏｎｇｓｈａｎＵｎｉｖｅｒｓｉｔｙ，Ｇｕａｎｇｚｈｏｕ，５１０２７５）Ａｂｓｔｒａｃｔ：Ｔ...     

Capability of Crossed Modules of Lie Algebras

In this paper, we introduce the concept of capability for crossed modules of Lie algebras, which is a generalization of capability in Lie algebras and groups. By using a special central ideal of a crossed module, we give a sufficient condition for the capability of a crossed module of Lie algebras. Also, we will extend the five-term exact sequence on homology of crossed modules of Lie algebras one term further and study the connection between the capability of crossed modules and this sequence. Finally, we study the relation between the capability and the center of a cover of a crossed module.     

限制Hamiltonian型及Contact型李代数的不可约表示

设L=H（2r;1）或K（2r+1;1）是定义在特征p>2的代数封闭域F上的限制Hamiltonian型或Contact型李代数.在对广义Jacobson-Witt代数及特殊代数不可约表示的研究基础上,通过定义L的如下阶化:L=L_[q],I,其中I是{1,2,…,r}的子集,得到当p-特征函数χ是正则半单时,所有不可约U_χ（L）-模都是从不可约U_χ(L_[O].I)-模诱导的.     

Critical Modules of the Ring of Differential Operators of an Affine Semigroup Algebra

Let D be the ring of differential operators of an affine semigroup algebra. Regarding the Krull dimension of finitely generated ? ^d -graded D-modules, we characterize critical ? ^d -graded D-modules. Moreover, we explicitly describe cyclic ones.