Part II. On antisymmetric homogeneous integral table algebras of degree three

Z. Arad; E. Fisman; V. Miloslavsky; M. Muzychuk

Part II. On antisymmetric homogeneous integral table algebras of degree three

Z. Arad, E. Fisman, V. Miloslavsky, M. Muzychuk

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2 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	54-73
Number of pages	20
Journal	Memoirs of the American Mathematical Society
Volume	144
Issue number	684
State	Published - 1 Mar 2000
Externally published	Yes

Keywords

C-algebra
Faithful element
Group algebra
Integral table algebra
Schur ring
Universal covering

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

Cite this

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AU - Fisman, E.

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AU - Muzychuk, M.

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Y1 - 2000/3/1

N2 - 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.

AB - 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.

KW - C-algebra

KW - Faithful element

KW - Group algebra

KW - Integral table algebra

KW - Schur ring

KW - Universal covering

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Part II. On antisymmetric homogeneous integral table algebras of degree three

Abstract

Keywords

ASJC Scopus subject areas

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