论文标题
Okubo自旋组的几何解释
A Geometrical Interpretation of Okubo Spin Group
论文作者
论文摘要
在这项工作中，我们首次定义了真正的Okubo代数上的仿射和投射平面，显示了其自旋组的具体几何解释。 Okubo代数是一个灵活的组成代数，也是一个不是Unitial Disecombra的代数。即使Okubo代数已闻名已有40多年，但我们认为这是代数首次用于仿射和投射几何形状。在证明了所有仿射几何形状的公理之后，我们在Okubo代数上定义了一个投影平面，作为仿射平面的完成，直接通过使用Veronese坐标。然后，我们在这两个构造之间提出了两者的培养。最后，我们显示了自旋（O）作为保留平面轴的一组的几何解释。
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.
