Theory of association schemes协会计划的理论 snb txt 网盘 pdf kindle 2025 lit 下载

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.

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

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 h

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