Completely reducible Lie subalgebras |
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Authors: | George McNinch |
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Affiliation: | (1) Department of Mathematics, Tufts University, 503 Boston Avenue, Medford, MA 02155, USA |
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Abstract: | 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. |
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