Ample Parabolic Subalgebras

作者：Leitner Felipe^*

来源：Journal of Lie Theory, 2015, 25(1): 233-255.

• Second-order homogeneous spaces
• nonlinear subalgebras
• structure theory of simple Lie algebras
• parabolic subalgebras

Let (L, L-0) be a finite-dimensional transitive pair of Lie algebras. We call the subalgebra L-0 ample nonlinear in L if its linear isotropy representation on L/L-0 admits a nontrivial kernel L-1, and the normalizer NL(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 ample parabolic subalgebras of L.

• 出版日期2015