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Homogeneous Integral Table Algebras of Degree Three: A Trilogy
 
Harvey I. Blau Northern Illinois University, DeKalb, IL
Bangteng Xu Northern Illinois University, DeKalb, IL
Z. Arad Bar-Ilan University, Ramat-Gan, Israel
E. Fisman Bar-Ilan University, Ramat-Gan, Israel
V. Miloslavsky Bar-Ilan University, Ramat-Gan, Israel
M. Muzychuk Bar-Ilan University, Ramat-Gan, Israel
Front Cover for Homogeneous Integral Table Algebras of Degree Three: A Trilogy
Available Formats:
Electronic ISBN: 978-1-4704-0275-4
Product Code: MEMO/144/684.E
List Price: $51.00
MAA Member Price: $45.90
AMS Member Price: $30.60
Front Cover for Homogeneous Integral Table Algebras of Degree Three: A Trilogy
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  • Back Cover for Homogeneous Integral Table Algebras of Degree Three: A Trilogy
Homogeneous Integral Table Algebras of Degree Three: A Trilogy
Harvey I. Blau Northern Illinois University, DeKalb, IL
Bangteng Xu Northern Illinois University, DeKalb, IL
Z. Arad Bar-Ilan University, Ramat-Gan, Israel
E. Fisman Bar-Ilan University, Ramat-Gan, Israel
V. Miloslavsky Bar-Ilan University, Ramat-Gan, Israel
M. Muzychuk Bar-Ilan University, Ramat-Gan, Israel
Available Formats:
Electronic ISBN:  978-1-4704-0275-4
Product Code:  MEMO/144/684.E
List Price: $51.00
MAA Member Price: $45.90
AMS Member Price: $30.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1442000; 89 pp
    MSC: Primary 13; 20; 05; 16;

    Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three.

    On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism of order three.

    Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.

    Readership

    Graduate students and research mathematicians interested in commutative rings and algebras.

  • Table of Contents
     
     
    • Chapters
    • I. Homogeneous integral table algebras of degree three with a faithful real element
    • II. On antisymmetric homogeneous integral table algebras of degree three
    • III. Homogeneous integral table algebras of degree three with no nontrivial linear elements
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Volume: 1442000; 89 pp
MSC: Primary 13; 20; 05; 16;

Homogeneous integral table algebras of degree three with a faithful real element. The algebras of the title are classified to exact isomorphism; that is, the sets of structure constants which arise from the given basis are completely determined. Other results describe all possible extensions (pre-images), with a faithful element which is not necessarily real, of certain simple homogeneous integral table algebras of degree three.

On antisymmetric homogeneous integral table algebras of degree three. This paper determines the homogeneous integral table algebras of degree three in which the given basis has a faithful element and has no nontrivial elements that are either real (symmetric) or linear, and where an additional hypothesis is satisfied. It is shown that all such bases must occur as the set of orbit sums in the complex group algebra of a finite abelian group under the action of a fixed-point-free automorphism of order three.

Homogeneous integral table algebras of degree three with no nontrivial linear elements. The algebras of the title which also have a faithful element are determined to exact isomorphism. All of the simple homogeneous integral table algebras of degree three are displayed, and the commutative association schemes in which all the nondiagonal relations have valency three and where some relation defines a connected graph on the underlying set are classified up to algebraic isomorphism.

Readership

Graduate students and research mathematicians interested in commutative rings and algebras.

  • Chapters
  • I. Homogeneous integral table algebras of degree three with a faithful real element
  • II. On antisymmetric homogeneous integral table algebras of degree three
  • III. Homogeneous integral table algebras of degree three with no nontrivial linear elements
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