Permutations of cubical arrays

[摘要] The structure constants of an algebra determine a cube called the cubical array associated with the algebra. The permuted indices of the cubical array associated with a finite semifield generate new division algebras. We do not not require that the algebra be finite and ask «Is it possible to choose a basis for the algebra such any permutation of the indices of the structure constants leaves the algebra unchanged?» What are the associated algebras? Author shows that the property «weakly quadratic» is invariant under all permutations of the indices of the corresponding cubical array and presents two algebras for which the cubical array is invariant under all permutations of the indices.

[发布机构] Department of Mathematics, University of Texas at San Antonio, 6900 North Loop 1604 West, San Antonio; TX; 78249-0697, United States^1

[效力级别] 数学

[关键词] Division algebras;Finite semifield;Structure constants