Permutations of cubical arrays

3Quantum: Algebra Geometry Information

物理学;数学

Wene, G.P.^1

Department of Mathematics, University of Texas at San Antonio, 6900 North Loop 1604 West, San Antonio

TX

78249-0697, United States^1

关键词: Division algebras;    Finite semifield;    Structure constants;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/532/1/012028/pdf
DOI  :  10.1088/1742-6596/532/1/012028

来源: IOP

【 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.