Completely reducible Lie subalgebras
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 of G. In this note, 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- September 2005
- DOI:
- 10.48550/arXiv.math/0509590
- arXiv:
- arXiv:math/0509590
- Bibcode:
- 2005math......9590M
- Keywords:
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- Mathematics - Representation Theory;
- Mathematics - Group Theory
- E-Print:
- 7 pages