of of classes of finite Properties products conjugacy groups 4r6radoldbrancf, This of finite was studied in the 1980's. The group theory. topic intensively book "Products of Classes in edited Z. Arad and [22] Conjugacy Groups," by M. a of the results obtained this Herzog, gives comprehensive picture during period. It realized several authors that this research could be extended to was by of irreducible characters. Werefer the reader to the products papers [1, 2, 11, 13-16,21,23,35,40,51,52,651. In several of these the authors found an between analogy pr- papers of classes and of irreducible characters which led to ucts conjugacy products of table introduced H.L.Blau and Z. Arad in in the notion algebra, by [7], in uniform the of of order to a decomposition products study way conjugacy and irreducible characters of finite Since the classes groups. then, theory in of Z. - of table was H. algebras extensively developed papers Arad, F. D. M.R. E. H. J. isha, Blau, B-dnger, Chillag, Darafsheh, Erez, Fisman, V. M. A. C. and B. Xu Miloslavsky, Muzychuk, Rahnamai, Scopolla [3-5,7- 10,12,17-20,25,29-33,35,41]. Table as be onsidered a class of defined, c special algbras, may C-algbras Y. Kawada and G. Hoheisel table introduced a by [49] [48].: More precisely, where the is a structure constants are Each algebra C-algebra nonnegative. finite two natural table the table of yields algebras: algebra conjugacy group classes and the table of characters.

lgrsnf/640.pdf

Christianity, Social Change, and Globalization in the Americas

Anna Lisa Peterson; Manuel A. Vásquez; Philip J. Williams

Ṣevî Ārād

Springer Spektrum. in Springer-Verlag GmbH

Steinkopff. in Springer-Verlag GmbH

Lecture notes in mathematics (Springer-Verlag), 1773, Berlin, Heidelberg, 2002

Lecture notes in mathematics <Berlin>, 1773, Berlin, 2002

1 edition, January 10, 2002

Germany, Germany

Lecture Notes in Mathematics
Preface
Contents
Introduction
1.1 Main Definitions
1.2 Basic examples
1.2.1 Association schemes and centralizer algebras
1.2.2 Schur rings
1.3 Basic properties
1.4 Basic constructions
1.4.1 The algebra T(n, $\lamda$, m)
1.4.2 Fusion and fission
1.4.3 Wreath, tensor and fibred products
Integral Table Algebras with a Faithful Nonreal Element of Degree 4
2.1 Known examples
2.1.1 Group-like algebras
2.1.2 The algebras F_m, F'_m
2.1.3 The algebra An(sgn)
2.2 Proof of the main results
2.2.1 Preclassification
2.2.2 Proof of Theorem I
2.2.3 Proof of Theorem 2
Standard Integral Table Algebras with a Faithful Nonreal Element of Degree 5
3.1 Introduction
3.2 General facts and known results
3.3 Degree 5
3.4 Case 3
3.5 Case 5
Standard Integral Table Algebras witha Faithful Real Element of Degree 5 andWidth 3
4.1 Introduction
4.2 Case 1
4.3 Case 2
The Enumeration of Primitive Commutative Association Schemes with a Non-symmetric Relation of Valency at Most 4
5.1 Introduction
5.2 The case of valency I or 2
5.3 The case of valency 3
5.4 The case of valency 4
References
Index

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.

Aimed at researchers in the theory of table algebras and association schemes, this volume contains further developments in the theory of table algebras, a developing area of algebraic combinatorics. The book collects papers dealing with a classification problem for standard integral table algebras.

Zvi Arad, Mikhail Muzychuk (eds.). Includes Bibliographical References (p. [121]-123) And Index. Also Available In An Electronic Version.

Lecture Notes in Mathematics
Erscheinungsdatum: 04.12.2001

2024-04-11