Journal of Lie Theory 25 (2015), No. 1, 233--255
Copyright Heldermann Verlag 2015
Ample Parabolic Subalgebras
Felipe Leitner
Institut für Geometrie, Technische Universität, 01062 Dresden, Germany
Felipe.Leitner@tu-dresden.de
[Abstract-pdf]
\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 $L$.
Keywords: Second-order homogeneous spaces, nonlinear subalgebras, structure theory of simple Lie algebras, parabolic subalgebras.
MSC: 17B05, 17B70, 53C30, 57S20
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