Classification of the Absolute-Valued Algebras with Left-Unit Satisfying x2(x2)2 = (x2)2x2

Abdellatif Rochdi; Alassane Diouf; Maribel Ramirez

arxiv: 1109.0239 · v1 · pith:WHQ3EAZRnew · submitted 2011-09-01 · 🧮 math.RA

Classification of the Absolute-Valued Algebras with Left-Unit Satisfying x2(x2)2 = (x2)2x2

Alassane Diouf , Maribel Ramirez , Abdellatif Rochdi This is my paper

classification 🧮 math.RA

keywords algebrasabsolute-valuedasthastoleft-unitsatisfyingadditionalgebra

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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; \astC; H; \astH; \astH(i; 1); O; \astO; \astO(i; 1) the list is completed by two new algebras not yet specified in the literature.

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Classification of the Absolute-Valued Algebras with Left-Unit Satisfying x2(x2)2 = (x2)2x2

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