Overview

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.

Full Product Details

Author:   Paul-Hermann Zieschang
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2005
Dimensions:   Width: 15.50cm , Height: 1.60cm , Length: 23.50cm
Weight:   0.462kg
ISBN:  

9783642065569

ISBN 10:   3642065562
Pages:   284
Publication Date:   21 October 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

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.

Reviews

From the reviews: Theory of association schemes is a self-contained textbook. ... The theory of association schemes can be applied to Hecke algebras of transitive permutation groups, and the algebras are usually noncommutative. So this treatment is also good for group theorists. ... The book under review also contains many recent developments in the theory. (Akihide Hanaki, Mathematical Reviews, 2006 h)

"From the reviews: ""Theory of association schemes is a self-contained textbook. … The theory of association schemes can be applied to Hecke algebras of transitive permutation groups, and the algebras are usually noncommutative. So this treatment is also good for group theorists. … The book under review also contains many recent developments in the theory."" (Akihide Hanaki, Mathematical Reviews, 2006 h)"

From the reviews: Theory of association schemes is a self-contained textbook. ! The theory of association schemes can be applied to Hecke algebras of transitive permutation groups, and the algebras are usually noncommutative. So this treatment is also good for group theorists. ! The book under review also contains many recent developments in the theory. (Akihide Hanaki, Mathematical Reviews, 2006 h)

Author Information

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.

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