i was having a think about it this morning. the thing i find daunting/uneappealing about Octonions is that they don't have a matrix representation (whereas of course the standard model gauge group does), which makes them very strange and unfamiliar things. however, there is G2. and i remembered that some time ago i was playing around with complexified G2 wondering if i could get the standard model gauge group out of it. this started from the discovery that it's a manifold of special holonomy (Ricci flat) as a subgroup of SO(7,7). I didn't know how to get anything useful out of it though so i went in a different direction instead. But i'm wondering now after reading about your work if it implies that the standard model gauge group actually *is* a subgroup of complexified G2 afterall?
The pseudo-Riemannian Berger list doesn't seem to get quite so much attention in the literature but to me it's very intriguing.
Mrs Beanbag
npub19k…svmq6
2026-07-25 17:34:09 UTC
in reply to nevent1q…gykx
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wss://relay.momostr.pinkPublished at
2026-07-25 17:34:09 UTCEvent JSON
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"content": "i was having a think about it this morning. the thing i find daunting/uneappealing about Octonions is that they don't have a matrix representation (whereas of course the standard model gauge group does), which makes them very strange and unfamiliar things. however, there is G2. and i remembered that some time ago i was playing around with complexified G2 wondering if i could get the standard model gauge group out of it. this started from the discovery that it's a manifold of special holonomy (Ricci flat) as a subgroup of SO(7,7). I didn't know how to get anything useful out of it though so i went in a different direction instead. But i'm wondering now after reading about your work if it implies that the standard model gauge group actually *is* a subgroup of complexified G2 afterall?\n\nThe pseudo-Riemannian Berger list doesn't seem to get quite so much attention in the literature but to me it's very intriguing.",
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