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Apr 12, 2019 at 19:13 comment added Ali Taghavi I assume you mean the orientation preserving diffeomorphisms is a simple group, yes?
Apr 12, 2019 at 19:12 comment added Ali Taghavi @KlausNiederkrüger Thank you very much for your attention to my question and your comment. So you actualy answered the first part of my following question mathoverflow.net/questions/327214/…
Apr 11, 2019 at 13:34 comment added Klaus Niederkrüger What I wrote before is wrong: Take all vector fields that vanish on a chosen open subset $U\subset M$. This is an ideal, since the Lie bracket of any vector field with one of those will also vanish on the $U$. My apologies.
Apr 10, 2019 at 22:49 comment added Klaus Niederkrüger I lack deeper knowledge on this, but I remember reading somewhere that the diffeomorphism group is simple. I don't know if this is sufficient to say that the Lie algebra of all smooth vector fields is simple, but I would not be extremely surprised.
Apr 8, 2019 at 2:18 history edited Ali Taghavi CC BY-SA 4.0
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Apr 8, 2019 at 0:49 history edited Ali Taghavi CC BY-SA 4.0
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Apr 8, 2019 at 0:33 history asked Ali Taghavi CC BY-SA 4.0