代数及相关领域最新进展

出版时间：2009-1  出版社：高等教育出版社  作者：董崇英，李福安　著  页数：317  字数：250000  

内容概要

董崇英教授是杰出青年基金（B）的获得者。 他是国际上无限维李代数和顶点算子代数领域最杰出的数学家之一。     本书将介绍代数及领域相关的一些最新研究进展。具体说来，将讨论具c

书籍目录

PrefaceEiichi Bannai and Etsuko Bannai: Spherical Designs and Euclidean DesignsYu Chen: Minimal Representation Degree of Affine Kac-Moody GroupsHuah Chu, Shou-Jen Hu and Ming-chang Kang: A Rationality Problem of Certain A4 ActionZongduo Dai, Kunpeng Wang and Dingfeng Ye: Characterization of Multi-Continued Fractions for Multi-Formal Laurent SeriesYi Fang and Zongzhu Lin: Eulerian Trails and Hamiltonian Paths in Digraphs with Anti-involutionsRongquan Feng and Hongfeng Wu: Efficient Pairing Computation on CurvesWenbin Guo: Some Ideas and Results in Group TheoryTayuan Huang, Lingling Huang and Miaow-Ing Lin: On a Class of Strongly Regular Designs and Quasi-semisymmetric DesignsHuishi Li: F-Leading Homogeneous Algebras and Gr6bner BasesJianbo Liu and Kaiming Zhao: Automorphism Groups of Lie Algebras from Quantum ToriYucai Su: Quasifinite Representations of Some Lie Algebras Related to the Virasoro AlgebraGeorge Szeto and Lianyong Xue: On Galois Extensions with an Inner Galois GroupNanhua Xi: Representations of Algebraic Groups: Some Basics and ProgressesJiping Zhang and Zhikai Zhang: Brou6's Conjecture for Finite Groups with Abelian Sylow p-SubgroupsSujing Zhou and Dongdai Lin: An Interesting Member ID-based Group SignatureCurriculum Vitae and Publications of Zhexian Wan

章节摘录

　　The purpose of this paper is basically to giye a survey oil the theory ofspherical t-designs and Euclidean t-designs We will first recall the definitionsof spherical t-designs and Euclidean t-designs We discuss some examplesand look at the problem of finding and classifying tight spherical designsand tight Euclidean designs We plan to discuss the connection with thecuhatureformulas in nunlericalanalysis on one hand，and the connectionwith groups and sphere packing problems oil the other hand2000 Mathematics Subject Classification：primary 05E99；secondary05899，51M99，62K99Keywords：Euclidean designs，spherical designs，tight designs，associationschemes，universally optimal codes，Assmus-Mattson type theoremThis paper is an extended version of the talk titled“On Euclidean t-Designs”given bv the first author at the confeFence in honor of Professor Zhexian Wans80th birthday in Bering in August 18-20，2007，The abstract given above reflectsthe actual talk In the talk.we discussed extensively on the connections ofeubatureformulas in numerical analysis with the theory of spherical and Euclidean designsSince the exposition discussing this part was already written up in 090，we wil！nottreat this part much in this paper.