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06/24/2022, 07:12 AM
(This post was last modified: 06/25/2022, 07:23 AM by Catullus.)
What would happen if you defined a communitive multiplication for octonions as k^(log(k,a)+log(k,b)), for some k such as sqrt(2)?

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Sincerely: Catullus

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(06/24/2022, 07:12 AM)Catullus Wrote: What would happen if you defined a communitive multiplication for octonions as log(k,k^a+k^b), for some k such as sqrt(2)?

Something ridiculous. You would still have a noncommutative ring of octonions. But now you attach a secondary commutative group, written based off of analytic operators you'd have to prove exist in the first place. I imagine asking this for quaternions would be hard enough. Instead of asking, perhaps look into how to solve it of your own accord.