The relations between Hilbert spaces over octonions and Hilbert spaces over Clifford algebras are discussed. It is shown that the category of Hilbert \(\mathbb {O}\)-bimodules is isomorphic to the category of Hilbert left \(C\ell _{6}\)-modules, and the category of Hilbert left \(\mathbb {O}\)-modules is isomorphic to the category of Hilbert left \(C\ell _{7}\)-modules.

中文翻译：

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八元数上的希尔伯特空间和克利福德代数上的希尔伯特空间之间的范畴同构

讨论了八元数上的希尔伯特空间和克利福德代数上的希尔伯特空间之间的关系。证明了 Hilbert \(\mathbb {O}\) -bimodules 的范畴与 Hilbert left \(C\ell _{6}\) -modules 的范畴同构，Hilbert left \(\ mathbb {O}\) -modules 与 Hilbert left \(C\ell _{7}\) -modules的范畴同构。