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In algebra, an Okubo algebra or pseudo-octonion algebra is an 8-dimensional non-associative algebra similar to the one studied by . Okubo algebras are composition algebras, flexible algebras (''A''(''BA'') = (''AB'')''A''), Lie admissible algebras, and power associative, but are not associative, not alternative algebras, and do not have an identity element. Okubu's example was the algebra of 3 by 3 trace zero complex matrices, with the product of ''X'' and ''Y'' given by ''aXY'' + ''bYX'' – Tr(''XY'')''I''/3 where ''I'' is the identity matrix and ''a'' and ''b'' satisfy ''a'' + ''b'' = 3''ab'' = 1. The Hermitian elements form an 8-dimensional real non-associative division algebra. A similar construction works for any cubic alternative separable algebra over a field containing a primitive cube root of unity. An Okubo algebra is an algebra constructed in this way from the trace 0 elements of a degree 3 central simple algebra over a field. ==References== * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Okubo algebra」の詳細全文を読む スポンサード リンク
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