Timeline for On the full reducibility of representations of reductive Lie algebras
Current License: CC BY-SA 2.5
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2010 at 0:58 | answer | added | Victor Protsak | timeline score: 4 | |
| Apr 30, 2010 at 14:07 | comment | added | José Figueroa-O'Farrill | I edited the title -- if the question is going to remain open, then at the very least it ought to have a title which conveys some information. | |
| Apr 30, 2010 at 14:07 | history | edited | José Figueroa-O'Farrill | CC BY-SA 2.5 |
The original title had no information. The present title is not a question, but it is more appropriate.
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| Apr 30, 2010 at 11:31 | answer | added | José Figueroa-O'Farrill | timeline score: 3 | |
| Apr 30, 2010 at 11:14 | vote | accept | Michele Torielli | ||
| Apr 30, 2010 at 10:44 | answer | added | Jim Humphreys | timeline score: 22 | |
| Apr 30, 2010 at 10:33 | comment | added | Robin Chapman | In his textbook, Humphreys sets as an exercise that a finite-dimensional representation of a reductive Lie algebra $L$ is completely reducible if every element in the centre of $L$ acts as a semisimple endomorphism. | |
| Apr 30, 2010 at 9:55 | answer | added | Homology | timeline score: 4 | |
| Apr 30, 2010 at 9:55 | comment | added | Michele Torielli | ok. thanks. do you know then some restriction to impose to the $\mathfrak{g}$-module in such that it's semisimple? | |
| Apr 30, 2010 at 9:48 | comment | added | Pete L. Clark | Robin is correct. Note that wikipedia states this result (and is therefore incorrect): en.wikipedia.org/wiki/… | |
| Apr 30, 2010 at 9:44 | comment | added | Michele Torielli | I meant: If we call $\mathfrak{g}$ the Lie algebra, is it true that every finite dimensional $\mathfrak{g}$-module is semisimple? | |
| Apr 30, 2010 at 8:45 | comment | added | Robin Chapman | Does "semisimple" for representations mean "completely reducible"? If so this is false as the only Lie algebras for which all finite-dimensional representations are completely reducible are the semisimple Lie algebras. | |
| Apr 30, 2010 at 8:24 | comment | added | François G. Dorais | Note that the result in question is short enough to be mentioned in the title. Generic titles are not very helpful. | |
| Apr 30, 2010 at 8:18 | history | asked | Michele Torielli | CC BY-SA 2.5 |