Noether环上的＊-模、余＊-模及cotilting模

设R为Noether环,讨论了R上*-模的投射性和内射性,引进与*-模相对偶的概念:余*-模,给出了R上余*-模的特征性质,最后用余*-模给出了R上cotilting模的刻划.     

一类基于量子环面非交换结合代数的模

在量子环面[1]上构造一类非交换结合代数AQ-模M(a,b),我们还刻划了AQ-模的结构并揭示[2]一类商模序列:每个商模Mn(a)/Mn+1(a)都同构于M(a,0),每个商模的自同构群AutMn(a)/Mn+1(a)均与C*同构.     

Noether模的Artin根

本文定义了Ｎｏｃｔｈｅｒ模的Ａｒｔｉｎ根，给出了Ｎｏｃｔｈｅｒ半局部环上有限生成模的Ａｒｔｉｎ根的刻划．最后，作为Ａｒｔｉｎ根理论的应用，给出了一个关于Ｃｏｈｅｎ－Ｍａｃａｕｌａｙ环的定理及一个模的用ｄｅｐｔｈ和ｋｒｕｌｌ维数表示的公式。     

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．     

一类量子环面李代数的单性(英文)

令C_q:=C_q[t₁^±1,t₂^±1,t₃^±1]为量子环面结合代数,L_q=C_q/C为量子环面李代数。本文定义了一个与q=（qij）_i,j=1³相关的指数方程体系,称之为C_q的特征方程组。通过这个特征方程组,证明了L_q是非单的当且仅当特征方程组在Z³中有非零解。对于|q|=0,证明了在C_q中存在一个极大交换子代数I,并且I严格包含中心Z（C_q）。同时文中也指出,对于|q|≠0,在C_q中不存在这样的子代数。     

Artin模的自同态环

本文讨论Ａｒｔｉｎ模的自同态环何时为半完全环的问题．对于Ａｒｔｉｎ模ＭＲ，本文证明了：（１）若Ｍ是非单的直和不可分解模，则ｓｏｃＭ为见的小子模；（２）对任意Ａｒｔｉｎ模Ｍ及任意Ａｒｔｉｎ半单模Ｌ，ＥｎｄＲ（ＭＬ）为半完全环的充要条件为ＥｎｄＲ（Ｍ）是半完全环．本文还证明了（直和不可分解的）拟投射Ａｒｔｉｎ模的自同态环为（局部环）半准素环．而对于非零的Ａｒｔｉｎ投射模Ｐ，“Ｐ直和不可分解”等价于“Ｐ和不可分解”．     

Noether环上的幂稳定自由模

设I是Noether环R的投射理想, I^m=Iⁿ, m≠n. 该文证明, 有限生成投射右R - 模幂稳定自由当且仅当(1) 存在环S使得I^|m-n|( S ( R且有限生成投射S - 模是幂稳定自由; (2) 有限生成投射右R/I^|m-n| - 模幂稳定自由.     

扭量子环面李代数L(C)Q[σ]的代数结构

L(C)Q[б]是由Eij(○×)Ekl(○×)t01/2+α0(m'-1)+l-kt1/2+α,1≤i,j≤m,1≤k,l≤m',(1/2)+α=(1/2+α0,…,1/2+αv)∈(1/2+Z)v+1生成的(Mm(C)(○×)Mlm(C))(C)Q[б]的扭量子环面李代数,研究L(C)Q[б]的代数结构.     

一类量子环面李代数的泛中心扩张

设Cq=Cq[x1^±1,x2^1]为复数域上的量子环面,其中q≠0是一个非单位根．D（Cq）为Cq的导子李代数．记Lq为Cq＋D（Cq）的导出子代数．本文研究李代数Lq的泛中心扩张．     

Periodic modules over general quantum Laurent polynomials

We construct, by induction on the number of variables, periodic finitely generated modules over general quantum Laurent polynomials. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 10–17, January, 1997. Translated by A. I. Shtern     

Indecomposable modules of the intermediate series over W(a, b)

For any complex parameters a and b,W(a,b)is the Lie algebra with basis{Li,Wi|i∈Z}and relations[Li,Lj]=(j i)Li+j,[Li,Wj]=(a+j+bi)Wi+j,[Wi,Wj]=0.In this paper,indecomposable modules of the intermediate series over W(a,b)are classified.It is also proved that an irreducible Harish-Chandra W(a,b)-module is either a highest/lowest weight module or a uniformly bounded module.Furthermore,if a∈/Q,an irreducible weight W(a,b)-module is simply a Vir-module with trivial actions of Wk’s.     

Classification of Quasifinite Modules with Nonzero Central Charges for EALAs of Type A with Coordinates in Quantum Torus

The author first constructs a Lie algebra ∑ ：=∑（q, Wd） from rank 3 quantum torus, which is isomorphic to the core of EALAs of type Ad-1 with coordinates in quantum torus Cqd, and then gives the necessary and sufficient conditions for the highest weight modules to be quasifinite nonzero central charges are Finally the irreducible Z-graded quasifinite ∑-modules with classified.     

非有限阶化无中心Virasoro超代数的表示

介绍非有限阶化无中心Virasoro超代数的概念,并通过具体计算给出了非有限阶化无中心Virasoro超代数的一类中间序列模.     

非阶化Virasoro代数和Virasoro超代数及其中间序列模

介绍非阶化Virasoro(超)代数的概念,给出非阶化Virasoro(超)代数的中间序列模,并对非阶化Virasoro代数的子代数(秩为1的非阶化Witt代数)的中间序列模进行分类．     

A uniform bound of reducibility index of good parameter ideals for certain class of modules

Let $(R,\mathfrak{m})$ be a Noetherian local ring and M a finitely generated R-module. The invariants $\mathrm{p}(M)$ and $\mathrm{sp}(M)$ of M were introduced in [3] and [17] in order to measure the non-Cohen–Macaulayness and the non-sequential-Cohen–Macaulayness of M, respectively. Let $M=D_0?D_1?\dots ?D_k$ be the filtration of M such that $D_i$ is the largest submodule of M of dimension less than $\dim ?D_{i?1}$ for all $i\le k$ and $\mathrm{p}(D_k)\le 1$. In this paper we prove that if $\mathrm{sp}(M)\le 1$, then there exists a constant c such that ${\mathrm{ir}}_M(\mathfrak{q}M)\le c$ for all good parameter ideals $\mathfrak{q}$ of M with respect to this filtration. Here ${\mathrm{ir}}_M(\mathfrak{q}M)$ is the reducibility index of $\mathfrak{q}$ on M. This is an extension of the main results of [19], [20], [24].     

On classification of quasifinite representations of two classes of Lie superalgebras of block type

Motivated by a well-known theorem of Mathieu’s on Harish–Chandra modules over the Virasoro algebra and its super version, we show that an irreducible quasifinite module over two classes of Lie superalgebras 𝒮(q) of Block type is either a highest or lowest weight module or else a module of the intermediate series if q≠?1. For such a module over 𝒮(?1), we give a rough classification.     

关于环Fpm+uFpm+u2Fpm上循环码的注记

本文研究了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码分类.通过建立环F_p^m+uF_p^m+u²F_p^m到环F_p^m+uF_p^m的同态,给出了环F_p^m+uF_p^m+u²F_p^m上长度为p^s的循环码的新分类方法.应用这种方法,得到了环F_p^m+uF_p^m+u²F_p^m长度为p^s的循环码的码词数.     

Simple modules of the quantum double of the Nichols algebra of unidentified diagonal type 𝔲𝔣𝔬(7)

The finite-dimensional simple modules over the Drinfeld double of the bosonization of the Nichols algebra 𝔲𝔣𝔬(7) are classified.