Completely reducible Lie subalgebras

Details Completely reducible Lie subalgebras Completely reducible Lie subalgebras

2005-09-25

arxiv.org/abs/math/0509590v2

Transformation Groups, Volume 12, Number 1 / March, 2007

Mathematics

Representation Theory

7 pages; AMS LaTeX. To appear in *Transformation Groups*

Scientific paper

10.1007/s00031-005-1130-5

Let G be a connected and reductive group over the algebraically closed field
K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H
of G. In this note, we give a notion of G-complete reducibility -- G-cr for
short -- for Lie subalgebras of Lie(G), and we show that if the closed subgroup
H < G is G-cr, then Lie(H) is G-cr as well.

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