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A geometrical interpretation of Okubo spin group
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Orientador(es)
Resumo(s)
In this work we define, for the first time, the affine and projective plane over the real Okubo algebra, showing a concrete geometrical interpretation of its Spin group. Okubo algebra is a flexible, composition algebra which is also a not unital division algebra. Even though Okubo algebra has been known for more than 40 years, we believe that this is the first time the algebra was used for affine and projective geometry. After showing that all axioms of affine geometry are verified, we define a projective plane over Okubo algebra as completion of the affine plane and directly through the use of Veronese coordinates. We then present a bijection between the two constructions. Finally we show a geometric interpretation of Spin(O) as the group of collineations that preserve the axis of the plane.
Descrição
Palavras-chave
Okubo algebra Projective plane Sping group Symmetric composition Collineation Veronese
Contexto Educativo
Citação
Editora
Elsevier