实Cayley-Dickson代数的正交图。第二部分：基元素对的子图
Orthogonality graphs of real Cayley-Dickson algebras. Part II: The subgraph on pairs of basis elements
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中文总结 AI 辅助
该研究针对实Cayley-Dickson代数的基元素对构成的正交图，证明至少16维时两代数同构等价于其图同构，并给出从图提取代数Cayley-Dickson参数的算法。
中文摘要 AI 辅助
我们考虑任意实Cayley-Dickson代数的零因子，其分量均为标准基元素。我们归纳构造这些元素上的正交图。随后证明，当关注至少16维代数时，两个代数同构当且仅当它们的图同构。我们还提供了从代数的图中提取其Cayley-Dickson参数的算法。
英文摘要
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.
