Electronic ISBN:  9781470402754 
Product Code:  MEMO/144/684.E 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 144; 2000; 89 ppMSC: 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 (preimages), 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 fixedpointfree 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.ReadershipGraduate 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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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 (preimages), 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 fixedpointfree 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.
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