Levi components of parabolic subalgebras of finitary Lie algebras

Details Levi components of parabolic subalgebras of finitary Lie algebras Levi components of parabolic subalgebras of finitary Lie algebras

2010-08-02

arxiv.org/abs/1008.0311v2

Mathematics

Representation Theory

21 pages, Corollary 3.6 added

Scientific paper

We characterize locally semisimple subalgebras $\l$ of $\sl_\infty$, $\so_\infty$, and $\sp_\infty$ which are Levi components of parabolic subalgebras. Given $\l$, we characterize the parabolic subalgebras $\p$ such that $\l$ is a Levi component of $\p$. When the set of such self-normalizing parabolic subalgebras $\p$ is finite, we prove an estimate on its cardinality. We consider various examples which highlight the differences from the case of parabolic subalgebras of finite-dimensional simple Lie algebras.

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