We present an eight-dimensional even sub-algebra of the 2^4 = 16-dimensional associative Clifford algebra Cl(4,0) and show that its eight-dimensional elements denoted as X and Y respect the norm relation ||XY|| = ||X|| ||Y||, thus forming an octonion-like but associative normed division algebra.

中文翻译：

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八维八元式但结合规范的除法代数

我们提出了 2^4 = 16 维结合 Clifford 代数 Cl(4,0) 的八维偶数子代数，并表明其表示为 X 和 Y 的八维元素遵守范数关系 ||XY|| = ||X|| ||Y||，从而形成一个八元式但关联的赋范除代数。