Classification of the Absolute-Valued Algebras with Left-Unit Satisfying x2(x2)2 = (x2)2x2
Abstract
We show that every absolute-valued algebra with left-unit satisfying (x2; x2; x2) = 0 is finite-dimensional of degree at most 4: Next, we determine such an algebras. In addition to the already known algebras R; C; ; H; ; (i; 1); O; ; (i; 1) the list is completed by two new algebras not yet specified in the literature.
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