Some properties of octonion and quaternion algebras

[摘要] In 1988, J.R. Faulkner has given a procedure to construct an octonion algebra on a finite dimensional unitary alternative algebra of degree three over a field K. Here we use a similar procedure to get a quaternion algebra. Then we obtain some conditions for these octonion and quaternion algebras to be split or division algebras. Then we consider the implications of the found conditions to the underlying algebra, when K contains a cubic root of unity.

[学科分类] 数学（综合）

[关键词] Alternative algebra; Composition algebra; Division algebra; Flexible algebra; Hurwitz algebra; Power associative algebra.