Timeline for On the full reducibility of representations of reductive Lie algebras
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Apr 30, 2010 at 10:43 | comment | added | Homology | No, it is true for semisimple Lie algebras, as said above. If you want to apply this to a reductive Lie algebra in a particular case, you need to make sure that the center of the Lie algebra is mapped to semisimple endomorphisms. | |
| Apr 30, 2010 at 10:11 | comment | added | damiano | @Michele: The result that you want is false. The standard example of non-semisimple representation of an abelian Lie algebra is $\begin{pmatrix} 0 & \mathbb{C} \cr 0 & 0 \end{pmatrix}$. Serre gives precise conditions on when complete reducibility holds in Theorem VI.5.1 of the stated reference. | |
| Apr 30, 2010 at 9:58 | comment | added | Michele Torielli | so, in your opinion, the result is it true? | |
| Apr 30, 2010 at 9:55 | history | answered | Homology | CC BY-SA 2.5 |