Conversation

QC (in Berlin 7/29-??? w/ COVID

tfw a physicist says two lie groups are isomorphic when they mean their lie algebras are isomorphic

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@QiaochuYuan

idk if physicists know this but sometimes students read your papers and they get confused because you said a false thing about lie groups and who do they come to for help? me, motherfuckers

a general point of confusion is treating things that are isomorphic as equal

treating them as NOT equal can also be confusing tho lmao had a linear algebra book that confused the hell out of me bc it defined everything twice (once for linear maps and once for matrices)

Berarom

@rerarom

I think (if not please correct me) that QC was annoyed that physicists treat e.g. O(n) and SO(n) as isomorphic

yes i’m going off a tangent for some reason i never really understood lie groups

Berarom

@rerarom

ok I'll first put my zfchat and say: well they are manifolds that are also groups in a compatible way, like the circle. but I suspect your complaint is deeper than that

i think i’m used to being 100% comfortable with topics bc i overlearned them so anything where i’m not 100% comfortable i feel like a total idiot

all these details about how SU(3) is two copies of SU(2) or whatever (i don’t remember which one it is) and all these other relationships between groups i don’t remember