Transformation Groups

, Volume 12, Issue 1, pp 127–135

Completely reducible Lie subalgebras


DOI: 10.1007/s00031-005-1130-5

Cite this article as:
McNinch, G. Transformation Groups (2007) 12: 127. doi: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 ⊂ 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.

Copyright information

© Birkhauser Boston 2007

Authors and Affiliations

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

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