Timeline for Extensions of compact Lie groups

10 events

when toggle format	what		by	license	comment
S Mar 9, 2019 at 2:15	history	suggested	Shaun		Added a tag.
Mar 9, 2019 at 0:44	review	Suggested edits
S Mar 9, 2019 at 2:15
Mar 7, 2019 at 22:33	answer	added	Tsemo Aristide		timeline score: 5
Mar 7, 2019 at 17:40	comment	added	Peter Michor		See section 15 (pages 169-190) of mat.univie.ac.at/~michor/dgbook.pdf for a quite comprehensive discussion of extensions of Lie algebras and Lie groups, including the discrete case.
Mar 7, 2019 at 16:56	history	edited	rori	CC BY-SA 4.0	added 538 characters in body
Mar 7, 2019 at 16:05	history	edited	YCor		edited tags
Mar 7, 2019 at 16:03	comment	added	YCor		Sure. My comment addressed the question when you asked about being bijective, before you edited.
Mar 7, 2019 at 16:01	history	edited	rori	CC BY-SA 4.0	added 1 character in body
Mar 7, 2019 at 15:59	comment	added	YCor		For $T$ the circle group, $\mathrm{Ext}_{\mathrm{Grp}}(T,T)$ is huge (there are many non-abelian extensions), so clearly $\mathrm{Ext}_{\mathrm{TopGrp}}(T,T)\to\mathrm{Ext}_{\mathrm{Grp}}(T,T)$ is not surjective. (Here I write $\mathrm{Ext}_{\mathrm{TopGrp}}$ what you call $\mathrm{Ext}_{\mathrm{Lie}}$ since it's the same.) Also if $F$ is a nontrivial finite group $\mathrm{Ext}_{\mathrm{TopGrp}}(T,F)\to\mathrm{Ext}_{\mathrm{Grp}}(T,F)$ is not onto since $\mathrm{Ext}_{\mathrm{Grp}}(T,F)$ is huge too. I guess $\mathrm{Ext}_{\mathrm{TopGrp}}(G,H)\to\mathrm{Ext}_{\mathrm{Grp}}(G,H)$ is injective.
Mar 7, 2019 at 15:49	history	asked	rori	CC BY-SA 4.0