We consider zero divisors of an arbitrary real Cayley–Dickson algebra such that their components are both standard basis elements. We construct inductively the orthogonality graph on these elements. Then we show that, if we restrict our attention to at least 16-dimensional algebras, two algebras are isomorphic if and only if their graphs are isomorphic. We also provide an algorithm to retrieve the Cayley–Dickson parameters of an algebra from its graph.

中文翻译：

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真实 Cayley-Dickson 代数的正交图。第二部分：基元素对的子图

我们考虑任意实数 Cayley-Dickson 代数的零除数，使得它们的分量都是标准基元素。我们在这些元素上归纳构建正交图。然后我们证明，如果我们将注意力限制在至少16维代数，两个代数是同构的当且仅当它们的图是同构的。我们还提供了一种算法来从其图中检索代数的 Cayley-Dickson 参数。