Algebra and Applications

On Normalized Integral Table Algebras (Fusion Rings)

Generated by a Faithful Non-real Element of Degree 3

Authors: Arad, Z., Bangteng, X., Chen, G., Cohen, E., Haj Ihia Hussam, A., Muzychuk, M.

  • Offers current results through well-established methodology.
  • Generalizes the finite linear groups of degree 3, yet remains broad in scope.
  • Written by the world's leading expert in this area.
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About this book

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.

Reviews

From the reviews:

“In the book under review the authors’ aim is to classify normalized integral table algebras generated by a faithful non-real element of degree 3. To do this several cases appear and the authors examine each case carefully to prove the existence of the table algebra in question. … is well organized and will be beneficial to many researchers of finite group theory.” (Mohammad-Reza Darafsheh, Mathematical Reviews, Issue 2012 f)

Table of contents (5 chapters)

  • Introduction

    Arad, Zvi (et al.)

    Pages 1-7

  • Splitting of the Main Problem into Four Sub-cases

    Arad, Zvi (et al.)

    Pages 9-150

  • A Proof of a Non-existence of Sub-case (2)

    Arad, Zvi (et al.)

    Pages 151-185

  • Preliminary Classification of Sub-case (3)

    Arad, Zvi (et al.)

    Pages 187-241

  • Finishing the Proofs of the Main Results

    Arad, Zvi (et al.)

    Pages 243-271

Buy this book

eBook $89.00
price for USA (gross)
  • ISBN 978-0-85729-850-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.00
price for USA
  • ISBN 978-0-85729-849-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $119.00
price for USA
  • ISBN 978-1-4471-2703-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
On Normalized Integral Table Algebras (Fusion Rings)
Book Subtitle
Generated by a Faithful Non-real Element of Degree 3
Authors
Series Title
Algebra and Applications
Series Volume
16
Copyright
2011
Publisher
Springer-Verlag London
Copyright Holder
Springer-Verlag London Limited
eBook ISBN
978-0-85729-850-8
DOI
10.1007/978-0-85729-850-8
Hardcover ISBN
978-0-85729-849-2
Softcover ISBN
978-1-4471-2703-1
Series ISSN
1572-5553
Edition Number
1
Number of Pages
X, 274
Topics