Timeline for On the full reducibility of representations of reductive Lie algebras
Current License: CC BY-SA 2.5
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| May 6, 2010 at 10:21 | comment | added | Michele Torielli | In my case, I'm studying exactly the Lie algebra of an algebraic group.Can you please your statement more precise? what happens in this type of cases? | |
| Apr 30, 2010 at 12:24 | comment | added | Jim Humphreys |
This reinforces the fact that the notion of "reductive" for a Lie algebra in characteristic 0 has no intrinsic interest, unless you study the Lie algebra of a Lie (or algebraic) group and relate their representations carefully. For affine algebraic groups in any characteristic the notion of "reductive" group is more interesting because of Chevalley's Jordan decomposition and its preservation under rational representations. (But in characteristic $p$ you lose the connection with complete reducibility: a reductive group is "geometrically" reductive but rarely "linearly" reductive.)
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| Apr 30, 2010 at 11:31 | history | answered | José Figueroa-O'Farrill | CC BY-SA 2.5 |