Frontiers of Mathematics in China >

2019 , Vol. 14 >Issue 6: 1231 - 1258

DOI: https://doi.org/10.1007/s11464-019-0809-1

RESEARCH ARTICLE

Normalized integral table algebras generated by a faithful real element of degree 2 and having 4 linear elements

  • Yu LI ,
  • Guiyun CHEN
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  • School of Mathematics and Statistics, Southwest University, Chongqing 400715, China

Received date: 28 Aug 2019

Accepted date: 17 Dec 2019

Published date: 15 Dec 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We completely classify the normalized integral table algebra (A, B) generated by a faithful real element of degree 2 and having four linear elements.

Key words： Faithful; normalized; integral table algebra (ITA); normalized integral table algebra (NITA); classification

Cite this article

Yu LI , Guiyun CHEN . Normalized integral table algebras generated by a faithful real element of degree 2 and having 4 linear elements[J]. Frontiers of Mathematics in China, 2019 , 14(6) : 1231 -1258 . DOI: 10.1007/s11464-019-0809-1

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Arad Z, Arisha H, Fisman E, Muzychuk M. Integral standard table algebras with a faithful nonreal element of degree 3. J Algebra, 2000, 231(2): 473–483

DOI

2
Arad Z, Blau H I. On table algebras and application to _nite group theory. J Algebra, 1991, 138: 137–185

DOI

3
Arad Z, Erez Y, Muzychuk M. On homogeneous standard integral table algebras of degree 4. Comm Algebra, 2006, 34(2): 463–519

DOI

4
Arad Z, Fisman E, Blau H I. Table algebras and applications to products of characters in _nite groups. J Algebra, 1991, 138: 186–194

DOI

5
Arad Z, Muzychuk M. Standard Integral Table Algebras Generated by a Non-real Element of Small Degree. Berlin: Springer-Verlag, 2002

DOI

6
Arad Z, Xu B, Chen G, Hussam A H I, Muzychuk M. On Normalized Integral Table Algebras (Fusion Rings): Generated by a Faithful Non-real Element of Degree 3. London: Springer-Verlag, 2011

DOI

7
Blau H I. Quotient structures in C-algebra. J Algebra, 1995, 177: 297–337

DOI

8
Blau H I. Integral table algebras, a_ne diagrams, and the analysis of degree two. J Algebra, 1995, 178: 872–918

DOI

9
Blau H I. Homogeneous integral table algebras of degree two. Algebra Colloq, 1997, 4(4): 393–408

10
Blau H I. Integral table algebras and Bose-Mesner algebras with a faithful nonreal element of degree 3. J Algebra, 2000, 231(2): 484–545

DOI

11
Chen G, Arad Z. On four normalized table algebras generated by a faithful nonreal element of degree 3. J Algebra, 2005, 283: 457–484

DOI

12
James G, Liebeck M. Representations and Characters of Groups. Cambridge: Cambridge Univ Press, 2001

DOI

13
Li Y, Chen G. On normalized integral table algebras generated by a non-real faithful element of degree 2. Preprint

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