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Dec
1
comment algebraic groups and their Lie algebras
@Jim Humphreys: Thanks for the kind words. The argument I give also works without change if ${\rm{GL}}(V)$ is replaced with any linear algebraic $k$-group. I'm not sure how the argument in D-G may differ from this, as I have always avoided looking at anything in D-G whenever possible.
Nov
30
comment algebraic groups and their Lie algebras
@Andriy: Your necessity comment beyond the connected semisimple case above is not quite true: things work well for unipotent groups too (as noted at the end of my answer below).
Nov
30
revised algebraic groups and their Lie algebras
added 290 characters in body
Nov
30
answered algebraic groups and their Lie algebras
Nov
27
accepted Is the normalizer of a reductive subgroup reductive?