Abstract
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.
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Communicated by Uwe Kaehler.
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This work was supported by the NNSF of China (12171448)
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Huo, Q., Ren, G. Category Isomorphisms Between Hilbert Spaces Over Octonions and Hilbert Spaces Over Clifford Algebras. Adv. Appl. Clifford Algebras 32, 40 (2022). https://doi.org/10.1007/s00006-022-01221-3
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DOI: https://doi.org/10.1007/s00006-022-01221-3