Standard Integral Table Algebras Generated by a Non-real Element of Small Degree

This book is addressed to the researchers working in the theory of table algebras and association schemes. This area of algebraic combinatorics has been rapidly developed during the last decade. The volume contains further developments in the theory of table algebras. It collects several papers which deal with a classification problem for standard integral table algebras (SITA). More precisely, we consider SITA with a faithful non-real element of small degree. It turns out that such SITA with some extra conditions may be classified. This leads to new infinite series of SITA which has interesting properties. The last section of the book uses a part of obtained results in the classification of association schemes. This volume summarizes the research which was done at Bar-Ilan University in the academic year 1998/99. TOC:Introduction (Z. Arad, M. Muzychuk): Main Definitions; Basic Examples; Basic Properties, Basic Constructions.- ITA with a Faithful Nonreal Element of Degree 4 (Z. Arad, M. Muzychuk, H. Arisha, E. Fishman): Known Examples; Proof of the Main Results.-SITA with a Faithful Nonreal Element of Degree 5 (Z. Arad, F. Bünger, E. Fishman, M. Muzuychuk): Introduction; General Facts and Known Results; Degree 5; Case 3; Case 5.- SITA with a Faithful Real Element of Degree 5 and Width 3 (F. Bünger): Introduction; Case 1; Case 2.- The Enumeration of Primitive Commutative Association Schemes (M. Hirasaka): Introduction; The Case of Valency 1 or 2; The Case of Valency 3; The Case of Valency 4.- References.-Index.

Introduction (Z. Arad, M. Muzychuk): Main Definitions; Basic Examples; Basic Properties, Basic Constructions.- ITA with a Faithful Nonreal Element of Degree 4 (Z. Arad, M. Muzychuk, H. Arisha, E. Fishman): Known Examples; Proof of the Main Results.-SITA with a Faithful Nonreal Element of Degree 5 (Z. Arad, F. Bünger, E. Fishman, M. Muzuychuk): Introduction; General Facts and Known Results; Degree 5; Case 3; Case 5.- SITA with a Faithful Real Element of Degree 5 and Width 3 (F. Bünger): Introduction; Case 1; Case 2.- The Enumeration of Primitive Commutative Association Schemes (M. Hirasaka): Introduction; The Case of Valency 1 or 2; The Case of Valency 3; The Case of Valency 4.- References.-Index.