Brauer代数的图子式(英文)

本文研究Brauer代数的根基问题.利用图子式的方法,获得了Gavarini的猜想对Brauer代数B1n是成立的结果.     

3g3维半单Hopf代数的结构

设g为素数,k是特征为零的代数闭域,日是k上的3q3维半单Hopf代数．本文证明了日总是半可解的,即H可由群代数或对偶群代数经过扩张得到．     

BCH-代数的闭理想

在BCH-代数中引入了闭理想的概念,并对其性质进行研究,得到了许多结果.     

Cartan矩阵的分解和Brauer特征标次数猜想

设G为有限群,N是G的正规子群.记J=J(F[N])为F[N]的Jacobson根,I=Ann(J)={α∈F[G]|Jα=0}为J在F[G]中的零化子.本文主要研究了,根据F[G/N]和F[G]/I的Cartan矩阵,分解F[G]的Cartan矩阵.这种分解在Cartan不变量和G的合成因子之间建立了一些联系.本文指出N中p-亏零块的存在性依赖于Cartan不变量或者I在F[G]中的性质,证明了Cartan矩阵的分解部分地依赖于B所覆盖的N中的块的性质.本文研究了b为N上的块且l(b)=1时,覆盖b的G中的块B的性质.在两类情形下,本文证明了块代数上关于Brauer特征标次数的猜想成立,涵盖了Holm和Willems研究的某些情形.进而对Holm和Willems提出的问题给出了肯定的回答.另外,本文还给出了Cartan不变量的一些其它结果.     

一类半单Hopf代数的结构

设k是特征为零的代数闭域,H是k上的pq~2维Frobenius型半单Hopf代数,其中p,q为不同的素数.本文证明了,如果p>q且H~*也是Frobenius型Hopf代数,则H是q~2维群代数A与A上p维Yetter-Drinfeld Hopf代数R的双积,即H≌R#A.作为例子,本文还证明了任意63维或68维的半单Hopf代数均为Frobenius型Hopf代数.     

基于弱Hopf代数的半单范畴的构造

本文研究并刻画了交换环上弱Hopf代数、Yetter-Drinfeld模范畴的一些性质,给出了其能够做成半单范畴的充分条件.     

Brauer第24问题的推广

本文对Ｂｒａｕｅｒ第２４问题［１］作了推广．利用Ｄａｄｅ关于循环块的理论得到如下结果：设Ｇ是有限群，Ｐ是Ｇ的循环Ｓｙｌｏｗｐ子群．设｜Ｐ｜＝ｐａ，ａ为正整数．令Ｐｉ为Ｐ中唯一的ｐｉ阶子群，１ｉａ．则｜Ｃｌ（Ｇ）｜＝｜Ｃｌ（ＮＧ（Ｐｉ））｜的充分必要条件为ＰｉＧ．     

有限群的Brauer特征标覆盖数

本文研究了有限群G的Brauer特征标覆盖数δ(G)问题.利用常特征标和Brauer特征标上的方法,获得了δ(G)是有限的当且仅当G/Op(G)是非交换单群这个结果,并进一步得到了当δ(G)有限时δ(G)的范围.     

关于Virasoro代数的2维上同调群

设g是特征数零的二次闭域K上的Virasoro代数,本文给出了系数在基本Harish-Chandra模中g的上同调群的一个成零条件和g的2维上同调群的结构。     

The equivariant Brauer group of a group

We consider the Brauer group of a group (finite or infinite) over a commutative ring with identity. A split exact sequence

is obtained. This generalizes the Fröhlich-Wall exact sequence from the case of a field to the case of a commutative ring, and generalizes the Picco-Platzeck exact sequence from the finite case of to the infinite case of . Here is the Brauer-Taylor group of Azumaya algebras (not necessarily with unit). The method developed in this paper might provide a key to computing the equivariant Brauer group of an infinite quantum group.

     

The Brauer group of Yetter-Drinfel'd module algebras

Let be a Hopf algebra with bijective antipode. In a previous paper, we introduced -Azumaya Yetter-Drinfel'd module algebras, and the Brauer group classifying them. We continue our study of , and we generalize some properties that were previously known for the Brauer-Long group. We also investigate separability properties for -Azumaya algebras, and this leads to the notion of strongly separable -Azumaya algebra, and to a new subgroup of the Brauer group .

     

A modified Brauer algebra as centralizer algebra of the unitary group

The centralizer algebra of the action of on the real tensor powers of its natural module, , is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for and with the decomposition of into irreducible submodules is considered.

     

项链李代数的性质

研究项链李代数的性质,给出了其中心元的表示形式,证明了项链李代数非半单、非可解,通过构造项链李代数的可解非幂零子代数,证明了当箭图中有长度大于1的循环时,项链李代数非幂零.还给出了没有圈的箭图上项链李代数的分解.     

A scheme related to the Brauer loop model

We introduce the Brauer loop scheme, where • is a certain degeneration of the ordinary matrix product. Its components of top dimension, ⌊N²/2⌋, correspond to involutions π∈SN having one or no fixed points. In the case N even, this scheme contains the upper-upper scheme from [A. Knutson, Some schemes related to the commuting variety, J. Algebraic Geom., in press, math.AG/0306275] as a union of (N/2)! of its components. One of those is a degeneration of the commuting variety of pairs of commuting matrices.The Brauer loop model is an integrable stochastic process studied in [J. de Gier, B. Nienhuis, Brauer loops and the commuting variety, J. Stat. Mech. (2005) P01006, math.AG/0410392], based on earlier related work in [M.J. Martins, B. Nienhuis, R. Rietman, An intersecting loop model as a solvable super spin chain, Phys. Rev. Lett. 81 (1998) 504-507, cond-mat/9709051], and some of the entries of its Perron-Frobenius eigenvector were observed (conjecturally) to equal the degrees of the components of the upper-upper scheme.Our proof of this equality follows the program outlined in [P. Di Francesco, P. Zinn-Justin, Inhomogeneous model of crossing loops and multidegrees of some algebraic varieties, math-ph/0412031]. In that paper, the entries of the Perron-Frobenius eigenvector were generalized from numbers to polynomials, which allowed them to be calculated inductively using divided difference operators. We relate these polynomials to the multidegrees of the components of the Brauer loop scheme, defined using an evident torus action on E. As a consequence, we obtain a formula for the degree of the commuting variety, previously calculated up to 4×4 matrices.     

On the Center of the Brauer Algebra

Using the determination of conjugacy classes in an earlier paper, we study the center of the Brauer algebra. In the case of finite groups, conjugacy class sums determine the center of the group algebra. In the case of the Brauer algebra the corresponding class sums only yield a basis of the centralizer of the symmetric group in the Brauer algebra. However, we exhibit an explicit algorithm to determine conditions for a centralizer element to be central and show how to compute a basis for the center using these methods. We will outline how this can be used to compute blocks over fields of arbitrary characteristic. We will also show that similar methods can be applied for computing a basis of the center of the walled Brauer algebra.