McKay箭图

Using the connection between McKay quiver and Loewy matrix,and the properties of characteristic polynomial of Loewy matrix,we give a generalized way to determine the McKay quiver for a finite subgroup of a generalized linear group.     

McKay箭图与m-Cartan矩阵

引入m-Cartan矩阵,并指出与Euclid图的Cartan矩阵的二次型的某些性质可以推广到McKay箭图的m—Cartan矩阵．还刻画了特殊线性群有限Abel子群的McKay箭图．     

McKay箭图与m-Cartan矩阵谨将本文献给刘绍学教授80华诞

引入m-Cartan矩阵,并指出与Euclid图的Cartan矩阵的二次型的某些性质可以推广到McKay箭图的m-Cartan矩阵.还刻画了特殊线性群有限Abel子群的McKay箭图.     

平移箭图ZΔ／（τ^p）的邻接矩阵

本文刻划了周期为P的稳定平移箭图ZΔ／（τ^p）的邻接矩阵，并给出了由星形箭图△所决定的平移箭图ZΔ／（τ^p）的邻接矩阵的具体形式．     

平移箭图Z△/(τ~p)的邻接矩阵

本文刻划了周期为p的稳定平移箭图Z△/(τp)的邻接矩阵,并给出了由星形箭图△所决定的平移箭图Z△/(τp)的邻接矩阵的具体形式.     

AR箭图一类连通分支的结构

给出了代数闭域上基连通有限维代数A的AR箭图中带有方向圈及不含有DT_r周期模且除投射-内射模外所含元均是左稳定模的一类连通分支的结构。     

由箭图构造的对偶Hopf代数和量子群

在文献[3]和[6]中,Hopf箭图的路代数上的Hopf代数结构和覆盖箭图的路余代数上的Hopf代数结构分别被给出.该文通过一个箭图是Hopf箭图当且仅当它是箭图覆盖这一结论,来讨论同一箭图上给出的这两种Hopf代数结构之间的对偶关系(见定理3和定理4).作为应用,作者先得到关于定向圈的路代数的商上的Hopf代数结构的一些性质,然后证明了Sweedler的4维-Hopf代数小仅是拟三角的而且是余拟三角的.最后,作者刻画了Schurian覆盖箭图的路代数上的Hopf代数的分次自同构群.     

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.     

含重边星形箭图偏周期预投射代数的希尔伯特级数

设△是一个有限无圈的箭图.引入了由△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△/(r^p)上的代数,记为Π_(Q(△,p),J).推广了Eting和Eu的方法并得到无圈的连通星形箭图△所决定的偏周期预投射代数Π_((Q(△,p)),J)的希尔伯特级数的计算公式.     

关于平移箭图上的截点圈

在本文中,我们证明了在一定条件下平移箭图中不存在截点圈(sectional cycle),从而推广了在阿丁代数的AR-箭图上Bautista和Smalφ的相应结果。     

Generalized McKay quivers of rank three

For each finite subgroup G of SLn（C）, we introduce the generalized Cartan matrix AG in view of McKay correspondence from the fusion rule of its natural representation. Using group theory, we show that the generalized Cartan matrices have similar favorable properties such as positive semi- definiteness as in the classical case of affine Cartan matrices. The complete McKay quivers for SL3 （C） are explicitly described and classified based on representation theory.     

On the McKay quivers and <Emphasis Type="Italic">m</Emphasis>-Cartan matrices

In this paper, we introduce the m-Cartan matrix and observe that some properties of the quadratic form associated to the Cartan matrix of an Euclidean diagram can be generalized to the m-Cartan matrix of a McKay quiver. We also describe the McKay quiver for a finite abelian subgroup of a special linear group. This work was supported by National Natural Science Foundation of China (Grant No. 10671061) and the Research Foundation for Doctor Programme (Grant No. 200505042004)     

Arc-smooth generalized universal covering spaces

Let Y be a path-connected subset of a CAT(0) space Z, allowing for a map to a 1-dimensional separable metric space X, such that the nontrivial point preimages of f form a null sequence of convex subsets of Z. Such Y need not be homotopy equivalent to a 1-dimensional space.

We prove that Y admits a generalized universal covering space, which we equip with an arc-smooth structure by consistently and continuously selecting one tight representative from each path homotopy class of Y. It follows that all homotopy groups of Y vanish in dimensions greater than 1.     

Compactifying sufficiently regular covering spaces of compact 3-manifolds

In this paper it is proven that if the group of covering translations of the covering space of a compact, connected, -irreducible 3-manifold corresponding to a non-trivial, finitely-generated subgroup of its fundamental group is infinite, then either the covering space is almost compact or the subgroup is infinite cyclic and has normalizer a non-finitely-generated subgroup of the rational numbers. In the first case additional information is obtained which is then used to relate Thurston's hyperbolization and virtual bundle conjectures to some algebraic conjectures about certain 3-manifold groups.     

McKay correspondence and orbifold equivalence

We prove that a pair of singularities related by a transformation arising from the McKay correspondence are orbifold equivalent. From this we deduce a McKay type category equivalence for the matrix factorization categories.     

覆盖近似空间的连续与同胚映射

利用一般映射研究了覆盖近似空间的一些性质,并证明了一些结论.接着定义了覆盖空间的粗糙连续映射及粗糙同胚映射.最后在覆盖粗糙连续映射和覆盖粗糙同胚映射的条件下,研究了两个覆盖近似空间的有关性质,进而在某种程度上为覆盖近似空间的分类提供了理论依据.     

Higher dimensional cable knots and their finite cyclic covering spaces

As an analogue of the classical cable knot, the p-cable n-knot about an n-knot K, where p is an integer and n?2, is defined, and some basic properties of higher dimensional cable knots are described. We show that for p>0 then p-fold branched cyclic covering space of an (n+2)-sphere branched over the p-cable knot about an n-knot K is an (n+2)-sphere or a homotopy (n+2)-sphere which is the result of Gluck-surgery on the composition of p copies of K according as if p is odd or even. At the same time, we prove that for any n?2 and p?2, the composition of p copies of any n-knot K is the fixed point set of a Z_p-action on an (n+2)-sphere. This is another counterexample to the higher dimensional Smith conjecture.