Transformation Groups

, Volume 12, Issue 1, pp 127–135 | Cite as

Completely reducible Lie subalgebras

  • George McNinch


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.


Normal Subgroup Algebraic Group Parabolic Subgroup Reductive Group Maximal Torus 
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Copyright information

© Birkhauser Boston 2007

Authors and Affiliations

  1. 1.Department of Mathematics, Tufts University, 503 Boston AvenueMedford, MA 02155USA

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