Theory of association schemes协会计划的理论
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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