> < ^ Date: Fri, 30 May 2003 14:28:40 +0200
< ^ From: Jan Draisma <Jan.Draisma@unibas.ch >
< ^ Subject: Re: All subalgebras of the given algebra

Dear Gap Forum, and Ilya,

> How can I get all subalgebras (up to isomorphism) of given Lie algebra?
In general, this seems a difficult task to me. The maximal subalgebras
of simple Lie algebras, however, have been classified by Dynkin (see refs
below). They are either reductive or parabolic. The latter can be computed
easily from the root data, and I wrote some code producing all classes
of maximal reductive subalgebras of classical Lie algebras, in LiE; see:


To use this, you should download LiE from:


(Restricting to classical Lie algebras, there are a few obvious maximal
subalgebras, such as o_n and sp_n in sl_n and o_n x o_m in o_{n+m},
and the other inclusions are of the form l->(o_n, sp_n or sl_n), where
l is a simple Lie algebra, embedded into the classical Lie algebra by
an irreducible module in which a symmetric, a skew symmetric, or no
bilinear form is l-invariant. My LiE-program produces the highest weight
of such a realisation, which could then be used in GAP to construct the
corresponding Lie algebra using HighestWeightModule.)

Best regards,

Jan Draisma

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