Talk:Lie algebra

message: I am not familiar with Lie algebras, but I don't see how the anticommutativity follows from the bilinearity and alternativity properties alone, without the use of the Jacobi relation. Could a hint to why it does be added?  (Or could it be added that the Jacobi relation is also necessary).
When I show anticommutativity (using all three relations), I assume that the Lie bracket with any argument z and the zero element (0) of the vector space is 0, but I am not sure that this is true.
To whoever made an edit, thank you! A few more words (not even one line) and the article has probably been made clearer to many readers. — Preceding unsigned comment added by 130.225.98.190 (talk) 09:48, 27 August 2015 (UTC)
replies: text: Once upon a time (maybe it was removed??) there was an explicit discussion of this. Basically, if you try to write out every possible way that an associative algebra could work, you are forced into having only two choices. Bilinearity allows only one of these two possibilities. There are similar arguments that can be made in various other kinds of algebras (not just Lie algebras) and I've noticed that, more than once, that some of these were removed; one edit summary called them "pointless philosophical ruminations". Of course, as your question shows, they are not pointless at all. I reverted that one, but I can't go run around and try to police these kinds of (destructive) edits. Perhaps someone else can find/reconstruct this argument; it can be found in the better-written textbooks. 67.198.37.16 (talk) 19:43, 31 October 2020 (UTC)
thread_title:  Anticommutativity follows from what? 

message: It has been proposed that classical Lie algebras be merged here. 
*Oppose: I feel that they warrant an article of their own, much like classical group displays the unique status (application and mathematics-wise) of these groups. On the technical side, the classical Lie algebras can be treated in a surprisingly uniform manner. YohanN7 (talk) 08:36, 5 May 2017 (UTC)
thread_title:  Merge proposal for Classical Lie algebras 

message: Hello fellow Wikipedians,
I have just modified one external link on Lie algebra. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20100420004313/http://math.mit.edu/~lesha/745lec/ to http://www.math.mit.edu/~lesha/745lec/
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 11:55, 15 May 2017 (UTC)
thread_title:  External links modified 

message: At the end of the intro, we find ...
This is the Lie algebra of the Lie group of rotations of space, and each vector v\in\R^3 may be pictured as an infinitesimal rotation around the axis v, with velocity equal to the magnitude of v.
My concern is that the magnitude of v represents the angle (or magnitude) of the rotation, not its velocity.
Am not confident enough in my concern to edit the page, hence am adding this topic, here.
Any thoughts? WadoNeil (talk) 10:24, 12 April 2023 (UTC)
replies: text: As the velocity mentioned at the end of the sentence is not related to anything, I think that the module of v might stand for the angle of rotation than for the velocity. Stefan Groote (talk) 05:01, 13 April 2023 (UTC)
thread_title:  Rotation Velocity Concern