The crucial properties that D(a) needs to satisfy in order to get an automorphism are:
D(a c) = a D(c) + D(a) = c D(a) + D(c)
D(1) = 0
while D(a) = 0 for all a is ruled out, because then the automorphism is inner.
Greg Egan
npub12c…gd38p
2025-03-16 22:50:02 UTC
in reply to nevent1q…jfx6
Author Public Key
npub12cuzzqzv8e8y7na77a9zv47mx2v6pec60qs5h7takzmv5p0mw0fsmgd38pPublished at
2025-03-16 22:50:02 UTCEvent JSON
{
"id": "e1eb5e95f8bf021a967980d92bdf260c14579083bfef15ea31b303fa386c5659",
"pubkey": "563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3",
"created_at": 1742165402,
"kind": 1,
"tags": [
[
"p",
"e6e109a519bafc96495a11ac9ee81e375a907144a2eab0b9d1f60065d5b9bf53"
],
[
"e",
"17df2d9e518f7b17c449ccb1609e0df72f3f3fd005ec7098144f5bd8c3f8c367",
"",
"reply",
"563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3"
],
[
"p",
"563821004c3e4e4f4fbef74a2657db3299a0e71a78214bf97db0b6ca05fb73d3"
],
[
"p",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"proxy",
"https://mathstodon.xyz/@gregeganSF/114174551827869341",
"web"
],
[
"e",
"a4beab19db6cddb8e55e6c334995de4f3906f4005f2e8f008cd93d718915bfe5",
"",
"root",
"9a6a1a8eefd0b53d7e0c966ab35bd904151246f03b1be98fa0d2d0eeb4940320"
],
[
"proxy",
"https://mathstodon.xyz/users/gregeganSF/statuses/114174551827869341",
"activitypub"
],
[
"L",
"pink.momostr"
],
[
"l",
"pink.momostr.activitypub:https://mathstodon.xyz/users/gregeganSF/statuses/114174551827869341",
"pink.momostr"
],
[
"-"
]
],
"content": "The crucial properties that D(a) needs to satisfy in order to get an automorphism are:\n\nD(a c) = a D(c) + D(a) = c D(a) + D(c)\nD(1) = 0\n\nwhile D(a) = 0 for all a is ruled out, because then the automorphism is inner.",
"sig": "066902af9304666d3904b1f1a0edebe70e4e7075a240018d1e6981f93acdd9c7e9bd32a541471d3775b0857e24596138bc221ec7741d1d01dcaa4dbca06c246f"
}