Short Text Note by papalex (reply)

2025-10-15 09:51:30 UTC

As for the Moufang identities. Since

> * The invertible elements in any alternative ring or alternative algebra form a Moufang loop.*

The answer should be yes, bioctonions (which are just octonions and hence a unital composition algebra over \(\mathbb{C}\) and thus invertible except for 0) form a Moufang loop. So the identities hold.

See second example in: https://ncatlab.org/nlab/show/Moufang+loop

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2025-10-15 09:51:30 UTC

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papalex on Nostr: As for the Moufang identities. Since > * The invertible elements in any alternative ...