Theory of association schemes协会计划的理论

Theory of association schemes协会计划的理论  点此进入淘宝搜索页搜索
  特别声明:本站仅为商品信息简介,并不出售商品,您可点击文中链接进入淘宝网搜索页搜索该商品,有任何问题请与具体淘宝商家联系。
  參考價格: 点此进入淘宝搜索页搜索
  分類: 图书,进口原版书,人文社科 Non Fiction ,

作者: Paul-Hermann Zieschang 著

出 版 社: 北京燕山出版社

出版时间: 2005-12-1字数:版次: 1页数: 283印刷时间: 2005/12/01开本: 16开印次: 1纸张: 胶版纸I S B N : 9783540261360包装: 精装内容简介

Theory of Association Schemes is the first concept-oriented treatment of the structure theory of association schemes. It contains several recent results which appear for the first time in book form. The generalization of Sylow’s group theoretic theorems to scheme theory arises as a consequence of arithmetical considerations about quotient schemes. The theory of Coxeter schemes (equivalent to the theory of buildings) emerges naturally and yields a purely algebraic proof of Tits’ main theorem on buildings of spherical type. Also a scheme-theoretic characterization of Glauberman’s Z*-involutions is included. The text is self-contained and accessible for advanced undergraduate students.

作者简介

Paul-Hermann Zieschang received a Doctor of Natural Sciences and the Habilitation in Mathematics from the Christian-Albrechts-Universität zu Kiel. He is also Extraordinary Professor of the Christian-Albrechts-Universität zu Kiel. Presently, he holds the position of an Associate Professor at the University of Texas at Brownsville. He held visiting positions at Kansas State University and at Kyushu University in Fukuoka.

目录

1 Basic Facts

1.1 Structure Constants

1.2 Symmetric Elements

1.3 The Complex Product

1.4 Complex Products and Valencies

1.5 Complex Products of Subsets of Cardinality 1

2 Closed Subsets

2.1 Basic Facts

2.2 Dedekind Identities

2.3 Structure Constants

2.4 Maximal Closed Subsets

2.5 Normalizer and Strong Normalizer

2.6 Conjugates of Closed Subsets

3 Generating Subsets

3.1 Basic Facts

3.2 The Thin Residue

3.3 Elements of Valency 2

3.4 Closed Subsets Generated by Involutions

3.5 Basic Results on Constrained Sets of Involutions.

3.6 Basic Results on Coxeter Sets

4 Quotient Schemes

4.1 Basic Definitions

4.2 General Facts

4.3 Valencies

4.4 Hall Subsets

4.5 Sylow Subsets

5 Morphisms

5.1 Basic Facts

5.2 Isomorphisms

5.3 The Isomorphism Theorems

5.4 Composition Series

5.5 The Group Correspondence

5.6 Residually Thin Schemes

6 Faithful Maps

6.1 Basic Facts

6.2 Faithfully Embedded Closed Subsets

6.3 The Schur Group of a Closed Subset

6.4 Elements of Valency 2

6.5 More About Elements of Valency 2

6.6 Constrained Sets of Involutions

6.7 Thin Thin Residues

7 Products

7.1 Direct Products of Closed Subsets

7.2 Quasidirect Products of Schemes

7.3 Semidirect Products

7.4 A Characterization of Semidirect Products

8 From Thin Schemes to Modules

8.1 Rings and Modules

8.2 Integrality in Associative Rings with 1

8.3 Completely Reducibility

8.4 Irreducible Modules over Associative Rings with 1

8.5 Semisimple Associative Rings with 1

8.6 Characters of Associative Rings with 1

8.7 Roots of Unity in Integral Domains

9 Scheme Rings

9.1 Basic Facts

9.2 Algebraically Closed Base Fields

9.3 Scheme Rings over the Field of Complex Numbers

9.4 Closed Subsets

9.5 Schemes with at most Five Elements

9.6 Constrained Sets of Involutions

10 Dihedral Closed Subsets

10.1 General Remarks

10.2 The Spherical Case

10.3 Arithmetic of the Length Function

10.4 Two Characteristic Subsets

10.5 The Constrained Spherical Case

10.6 Dihedral Closed Subsets of Finite Valency

11 Coxeter Sets

11.1 Parabolic Subsets

11.2 Direct Products

11.3 Faithful Maps

11.4 The Extension Theorem

12 Spherical Coxeter Sets

12.1 Elements of Maximal Length

12.2 Faithful Maps

12.3 The Main Theorem

12.4 Coxeter Schemes of Finite Valency and Rank 2 .

12.5 Valencies and Multiplicities

12.6 Polarities

References

Index

 
 
免责声明:本文为网络用户发布,其观点仅代表作者个人观点,与本站无关,本站仅提供信息存储服务。文中陈述内容未经本站证实,其真实性、完整性、及时性本站不作任何保证或承诺,请读者仅作参考,并请自行核实相关内容。
 
© 2005- 王朝網路 版權所有 導航