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Transformation Groups

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

Completely reducible Lie subalgebras

  • George McNinch
Article

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.

Keywords

Normal Subgroup Algebraic Group Parabolic Subgroup Reductive Group Maximal Torus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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