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# Theory of Association Schemes

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The present text is an introduction to the theory of association schemes. We start with the de?nition of an association scheme (or... Weiterlesen
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## Beschreibung

The present text is an introduction to the theory of association schemes. We start with the de?nition of an association scheme (or a scheme as we shall say brie?y), and in order to do so we ?x a set and call it X. We write 1 to denote the set of all pairs (x,x) with x? X. For each subset X ? r of the cartesian product X×X, we de?ne r to be the set of all pairs (y,z) with (z,y)? r.For x an element of X and r a subset of X× X, we shall denote by xr the set of all elements y in X with (x,y)? r. Let us ?x a partition S of X×X with?? / S and 1 ? S, and let us assume X ? that s ? S for each element s in S. The set S is called a scheme on X if, for any three elements p, q,and r in S, there exists a cardinal number a such pqr ? that|yp?zq| = a for any two elements y in X and z in yr. pqr The notion of a scheme generalizes naturally the notion of a group, and we shall base all our considerations on this observation. Let us, therefore, brie?y look at the relationship between groups and schemes.

Conceptual approach to association schemes is emphasized

First rigorous treatment of the structure theory of schemes. Schemes are considered not necessarily to be commutative or finite. As a byproduct, the theory covers (disguised as 'Coxeter schemes') the theory of buildings in the sense of Jacques Tits

Recent results such as the generalization of Sylow's group-theoretical theorems to scheme theory and the characterization of Glauberman's Z*-involutions in terms of scheme theory appear for the first time in book form

Autorentext

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.

Inhalt
Basic Facts.- Closed Subsets.- Generating Subsets.- Quotient Schemes.- Morphisms.- Faithful Maps.- Products.- From Thin Schemes to Modules.- Scheme Rings.- Dihedral Closed Subsets.- Coxeter Sets.- Spherical Coxeter Sets.

## Produktinformationen

 Titel: Theory of Association Schemes Autor: EAN: 9783642065569 ISBN: 3642065562 Format: Kartonierter Einband Herausgeber: Springer Berlin Heidelberg Anzahl Seiten: 300 Gewicht: 458g Größe: H235mm x B155mm x T16mm Jahr: 2010 Auflage: Softcover reprint of hardcover 1st ed. 2005

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