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On Normalized Integral Table Algebras (Fusion Rings)

Generated by a Faithful Non-real Element of Degree 3

  • Zvi Arad
  • Xu Bangteng
  • Guiyun Chen
  • Effi Cohen
  • Arisha Haj Ihia Hussam
  • Mikhail Muzychuk

Part of the Algebra and Applications book series (AA, volume 16)

Table of contents

  1. Front Matter
    Pages I-X
  2. Zvi Arad, Xu Bangteng, Guiyun Chen, Effi Cohen, Arisha Haj Ihia Hussam, Mikhail Muzychuk
    Pages 1-7
  3. Zvi Arad, Xu Bangteng, Guiyun Chen, Effi Cohen, Arisha Haj Ihia Hussam, Mikhail Muzychuk
    Pages 9-150
  4. Zvi Arad, Xu Bangteng, Guiyun Chen, Effi Cohen, Arisha Haj Ihia Hussam, Mikhail Muzychuk
    Pages 151-185
  5. Zvi Arad, Xu Bangteng, Guiyun Chen, Effi Cohen, Arisha Haj Ihia Hussam, Mikhail Muzychuk
    Pages 187-241
  6. Zvi Arad, Xu Bangteng, Guiyun Chen, Effi Cohen, Arisha Haj Ihia Hussam, Mikhail Muzychuk
    Pages 243-271
  7. Back Matter
    Pages 273-274

About this book

Introduction

The theory of table algebras was introduced in 1991 by Z. Arad and H.Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups.  Today, table algebra theory is a well-established branch of modern algebra with various applications, including  the representation theory of finite groups, algebraic combinatorics and fusion rules algebras.

This book presents the latest developments in this area.  Its main goal is to  give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification approach, while remaining parts separately treat special cases that appear during classification. A particularly unique contribution to the field, can be found in part four, whereby a number of the algebras are linked to the polynomial irreducible representations of the group SL3(C).

This book will be of interest to research mathematicians and PhD students working in table algebras, group representation theory, algebraic combinatorics and integral fusion rule algebras.

Keywords

fusion rings group representation theory integral fusion rules algebras table algebras

Authors and affiliations

  • Zvi Arad
    • 1
  • Xu Bangteng
    • 2
  • Guiyun Chen
    • 3
  • Effi Cohen
    • 4
  • Arisha Haj Ihia Hussam
    • 5
  • Mikhail Muzychuk
    • 6
  1. 1.Department of MathematicsBar-Ilan UniversityRamat GanIsrael
  2. 2.Department of Mathematics and StatisticsEastern Kentucky UniversityRichmondUSA
  3. 3.Department of MathematicsSouthwest UniversityChongqingChina, People's Republic
  4. 4.Department of MathematicsBar-Ilan UniversityRamat GanIsrael
  5. 5.Department of MathematicsAlqasemi AcademicCollege of EducationBaqa El-GharbiehIsrael
  6. 6.Netanya Academic CollegeNetanyaIsrael

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-850-8
  • Copyright Information Springer-Verlag London Limited 2011
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-85729-849-2
  • Online ISBN 978-0-85729-850-8
  • Series Print ISSN 1572-5553
  • Series Online ISSN 2192-2950
  • Buy this book on publisher's site