Hopf代数的半单扩张与不变子环的同调维数

设H是域k上的有限维Hopf代数,A是左H-模代数,AH是A的H-不变子环.假定A/AH是半单扩张且A是平坦的右AH-模.如果H*是unimodular,且存在c∈C(A),使t·c=1.我们证明了WD(AH)=WD(A)=WD(A#H).此外,如果A是投射的左及右AH-模,则有LD(AH)=LD(A)=LD(A#H).     

On the algebraicK-theory of twisted flag varieties

The algebraicK-groups of projective homogeneous varieties are computed. The answer is given in terms ofK-groups of a semisimple algebra canonically associated with the variety. Our results generalize a result of Quillen and a result of Swan, whereK-groups of Severi-Brauer varieties and of smooth projective quadratic hypersurfaces were computed.     

无机化学教学中以金课标准提升学生创新思维*——以形状记忆合金材料教学为例

基于教育部提出的“两性一度”的金课标准,在对形状记忆合金的发现历史和现状进行综述的过程中,融入镍钛合金为代表的形状记忆合金掺杂改性等问题分析,应用到无机化学元素内容教学中,并在创新设计的过程中进一步进行理论分析及实践例证。通过深入讨论其潜在应用领域及可能遇到的生产困难,提高学生理论-实践-创新的能力,培养学生创新思维。     

A Theorem of Truemper

Received November 5, 1997     

NOTE – Edge-Coloring Cliques with Many Colors on Subcliques

with colors in which the edges of every copy of together receive at least 3 colors. We prove that this construction also has the property that at least colors appear on the edges of every copy of for . Received August 11, 1998     

An Algebraic Matching Algorithm

V by V skew-symmetric matrix , called the Tutte matrix, associated with a simple graph G=(V,E). He associates an indeterminate with each , then defines when , and otherwise. The rank of the Tutte matrix is exactly twice the size of a maximum matching of G. Using linear algebra and ideas from the Gallai–Edmonds decomposition, we describe a very simple yet efficient algorithm that replaces the indeterminates with constants without losing rank. Hence, by computing the rank of the resulting matrix, we can efficiently compute the size of a maximum matching of a graph. Received September 4, 1997     

On the Signed Domination in Graphs

G on n vertices with minimum degree r, there exists a two-coloring of the vertices of G with colors +1 and -1, such that the closed neighborhood of each vertex contains more +1's than -1's, and altogether the number of 1's does not exceed the number of -1's by more than . As a construction by Füredi and Mubayi shows, this is asymptotically tight. The proof uses the partial coloring method from combinatorial discrepancy theory. Received May 12, 1998     

Bicliques in Graphs I: Bounds on Their Number

Bicliques are inclusion-maximal induced complete bipartite subgraphs in graphs. Upper bounds on the number of bicliques in bipartite graphs and general graphs are given. Then those classes of graphs where the number of bicliques is polynomial in the vertex number are characterized, provided the class is closed under induced subgraphs. Received January 27, 1997     

NOTE The Johnson Graphs Satisfy a Distance Extension Property

G has property if whenever F and H are connected graphs with and |H|=|F|+1, and and are isometric embeddings, then there is an isometric embedding such that . It is easy to construct an infinite graph with for all k, and holds in almost all finite graphs. Prior to this work, it was not known whether there exist any finite graphs with . We show that the Johnson graphs J(n,3) satisfy whenever , and that J(6,3) is the smallest graph satisfying . We also construct finite graphs satisfying and local versions of the extension axioms studied in connection with the Rado universal graph. Received June 9, 1998     

Coherent Continuation on the Category of (𝔤, K)-Modules

Abstract

Let 𝔤 be a complex semisimple Lie algebra. Let K be an algebraic group acting on the flag variety of 𝔤 with finitely many orbits. We give a geometric interpretation of the coherent continuation on the category of finitely generated (𝔤, K )-modules in terms of the intertwining functors on the category of K-equivariant 𝒟-modules.