Timeline for Is there any example of a Lie algebra which is not a derivation algebra?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Mar 17, 2022 at 19:53 | review | Suggested edits | |||
| Mar 17, 2022 at 20:16 | |||||
| Nov 2, 2021 at 14:53 | vote | accept | cos_dm_math21 | ||
| Oct 14, 2021 at 18:41 | comment | added | YCor | @SamHopkins but this would work equally for Lie algebras. I understand now the question as whether every $\mathfrak{g}$ is isomorphic to $\mathrm{Der}(A)$ for some unital associative algebra $A$ [or maybe just associative, or even arbitrary, OP should clarify]. This sounds quite clear when OP says "quite often defined as derivation algebras". A given Lie algebra such as $\mathfrak{gl}_n$ does not "define" all its subalgebras. | |
| Oct 14, 2021 at 18:37 | comment | added | Sam Hopkins | I guess there is actually an issue of whether the derivations of the matrix algebra in question are all inner (see math.stackexchange.com/questions/4205733/… for a related question) | |
| Oct 14, 2021 at 18:20 | comment | added | Sam Hopkins | So Ado's theorem answers the question in the affirmative, no? (Sorry, "affirmative" here is ambiguous: I mean it shows every finite-dimensional Lie algebra is realized as derivations of an associative algebra.) | |
| Oct 14, 2021 at 18:15 | comment | added | YCor | Ah indeed. The word "associative" would have been welcome earlier :) especially as the OP has only used the lie-algebra tag. | |
| Oct 14, 2021 at 18:13 | comment | added | Sam Hopkins | Isn't the OP asking about derivations of an associative algebra? | |
| Oct 14, 2021 at 18:01 | history | answered | YCor | CC BY-SA 4.0 |