Completely reducible Lie subalgebras
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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 ⊂ G. In this paper, 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.
KeywordsNormal Subgroup Algebraic Group Parabolic Subgroup Reductive Group Maximal Torus
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