星形箭图偏周期预投射代数的Hilbert级数

设△是一个有限无圈的箭图.引入了由Δ所决定的偏周期预投射代数,它是一个定义在周期为p的稳定平移箭图Z△/(τ~p)上的代数,记为Π_(Q(Δ,p),J).当周期p=1时,偏周期预投射代数就是偏预投射代数.我们推广了Eting和Eu的方法并得到无圈的星形箭图△所决定的偏周期预投射代数Π_((Q(Δ,p)),J)的Hilbert级数的计算公式.     

套代数中的检测问题

本文回答了套代数中的Ｋａｐｌａｎｓｋｙ检测问题，包括套代数的酉等价和同构．还将套代数的同构定理推广到套代数的直和代数上．     

ON Δ-GOOD MODULE CATEGORIES OF QUASI-HEREDITARY ALGEBRAS

A useful reduction is presented to determine the finiteness of △-good module category F(△)of a quasi-heredltary algebra. As an application of the reduction, the f(△)-finitenetess of quasi-hereditary M-twisted double incidence algebras of posets is discussed. In particular, a complete classification of F(△)-finite M-twisted double incidence algebras is given in case the posets are linearly ordered.     

李代数的Poisson代数结构Ⅱ

本文研究民具有无限维中心的Toroidal李代数.通过利用其明确的生成元,确定了其上所有的非交换Poisson代数结构,从而推广了有限维中心的情形.     

关于基础课程教材的现代化处理

以编著"高等代数"面向二十一世纪教材《线性代数导引》和对其第二版(英文版)的修订为例,从以下五个方面探讨基础课程教材的现代化处理:经典内容的尽量更新;经典内容的适当增新;增加一点公理化方法的对比使用;加强与初等数学内容的联系;加强理论与其背景的联系和强化核心概念.     

AR箭图,例外序列与导出Hall代数中的算法

如果半单Lie代数g和有限维遗传代数Λ对应于相同的Dynkin图,则有量子群U_q(g)的正部分U~+典范地同构于Hall代数H(Λ).一个自然的问题是:如何将U+中的根向量分解为Chevalley生成元的单项式的线性组合?Chen和Xiao给出的两种算法分别利用了Λ-模的例外序列上的辫子群作用以及Λ的Auslander-Reiten箭图的结构.对于To(e|¨)n定义的导出Hall代数,本文提出了类似的问题.并得到了相应的两种算法.这两种算法也同样适用于Kapranov定义的格代数和Heisenberg double.而且,所有新的递归公式都具有和量子Serre关系相似的形式.     

SU(1,1)线性非自治量子系统的代数动力学求解

利用代数动力学方法得到了SU(1,1)线性非自治量子系统的精确解及其Cartan不变算子,并建立和澄清了量子解与经典解之间的对应关系.另外还讨论了周期系统的非绝热和绝热Berry相因子. 关键词：     

n-李代数的结构

主要研究特征为2的代数闭域上(n+1)维n-李代数的结构,给出了(n+1)维n-李代数的分类,描述了其可解性与幂零性,刻画了(n+1)维n-李代数的导子代数与内导子代数的结构.     

Single Qubit and Its Universal Logic Gate Made of a Heisenberg Spin Cluster with Five Particles

We investigate an anisotropic Heisenberg spin cluster with five particles controlled by a time-dependent magnetic field. With the algebraic dynamical method, we obtain the exact analytical solution to the time dependent Schr6dinger equation. Based on the analytical solution, it is shown that the system can be used as a universal single qubit logic gate controlled by the strength and frequency of the magnetic field, and the six special single qubit logic gates can be realized physically. We also discuss the anti-decoherence property of the qubit and its logic gates resulted from particle coupling effect and collectivity of the cluster.     

Induced Lie Algebras of a Six-Dimensional Matrix Lie Algebra

By using a six-dimensional matrix Lie algebra [Y.F. Zhang and Y. Wang, Phys. Lett. A 360 （2006） 92], three induced Lie algebras are constructed. One of them is obtained by extending Lie bracket, the others are higher-dimensional complex Lie algebras constructed by using linear transformations. The equivalent Lie algebras of the later two with multi-component forms are obtained as well. As their applications, we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.