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Finishing the Proofs of the Main Results

  • Zvi AradEmail author
  • Xu Bangteng
  • Guiyun Chen
  • Effi Cohen
  • Arisha Haj Ihia Hussam
  • Mikhail Muzychuk
Chapter
  • 559 Downloads
Part of the Algebra and Applications book series (AA, volume 16)

Abstract

In this chapter the case (3) is almost classified by studying the remaining open case when b 3 b 10 contains two constituents and the elements b 10, b 15 are non-real. For this purpose we developed an elegant theory which enables us to generalize the Main Theorem of the book for NITA of countable dimension. The Main Theorem of this chapter almost classifies countable NITAs generated by a non-real basis element of degree 3 provided that any non-identical basis element has degree at least three.

References

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    Arad, Z., Blau, H.: On table algebras and applications to finite group theory. J. Algebra 138, 137–185 (1991) MathSciNetCrossRefzbMATHGoogle Scholar
  2. [AC]
    Arad, Z., Chen, G.: On four normalized table algebras generated by a faithful nonreal element of degree 3. J. Algebra 283, 457–484 (2005) MathSciNetCrossRefzbMATHGoogle Scholar
  3. [B]
    Blau, H.: Table algebras, Eur. J. of Comb. 30, 1426–1455 (2009) MathSciNetCrossRefzbMATHGoogle Scholar
  4. [M]
    Macdonald, I.G.: Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, 2nd edn. The Clarendon Press, Oxford University Press (1995) zbMATHGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

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

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