Journal of Lie Theory

no. 1
Ample Parabolic Subalgebras
Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 233-255
\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 $L$.
DOI: 10.5802/jolt.835
Classification: 17B05, 17B70, 53C30, 57S20
Keywords: Second-order homogeneous spaces, nonlinear subalgebras, structure theory of simple Lie algebras, parabolic subalgebras 
@article{JOLT_2015_25_1_a11,
     author = {F. Leitner},
     title = {Ample {Parabolic} {Subalgebras}},
     journal = {Journal of Lie Theory},
     pages = {233--255},
     year = {2015},
     volume = {25},
     number = {1},
     doi = {10.5802/jolt.835},
     zbl = {1394.17012},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.835/}
}
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F. Leitner. Ample Parabolic Subalgebras. Journal of Lie Theory, Volume 25 (2015) no. 1, pp. 233-255. doi: 10.5802/jolt.835

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