Ample Parabolic Subalgebras
Journal of Lie Theory, Tome 25 (2015) no. 1, pp. 233-255
Voir la notice de l'article provenant de la source Heldermann Verlag
\def\C{{\Bbb C}} \def\K{{\Bbb K}} \def\R{{\Bbb R}} Let $(L,L_0)$ be a finite-dimensional transitive pair of Lie algebras. We call the subalgebra $L_0$ {\it ample nonlinear} in $L$ if its linear isotropy representation on $L/L_0$ admits a nontrivial kernel $L_1$, and the normalizer $N_L(L_1)$ of that kernel is identical to $L_0$. For semisimple Lie algebras $L$ over $\K=\R,\C$, we classify in this paper the ample nonlinear subalgebras $L_0$. These subalgebras are exactly the {\it ample parabolic subalgebras} of $L$.
Classification :
17B05, 17B70, 53C30, 57S20
Mots-clés : Second-order homogeneous spaces, nonlinear subalgebras, structure theory of simple Lie algebras, parabolic subalgebras
Mots-clés : Second-order homogeneous spaces, nonlinear subalgebras, structure theory of simple Lie algebras, parabolic subalgebras
Affiliations des auteurs :
Felipe Leitner 1
Felipe Leitner. Ample Parabolic Subalgebras. Journal of Lie Theory, Tome 25 (2015) no. 1, pp. 233-255. http://geodesic.mathdoc.fr/item/JOLT_2015_25_1_a11/
@article{JOLT_2015_25_1_a11,
author = {Felipe Leitner},
title = {Ample {Parabolic} {Subalgebras}},
journal = {Journal of Lie Theory},
pages = {233--255},
year = {2015},
volume = {25},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2015_25_1_a11/}
}