[GAP Forum] subalgebras of simple lie algebras

[R.N. Tsai]

Dear gap-forum,
   
  Is there a way to look for subalgebras of certain type in a simple lie
algebra. Interestingly enough the example in the documentation is
very close to what I'm looking for :
   
  gap> L:= SimpleLieAlgebra( "E", 8, Rationals );;
gap> b:= BasisVectors( Basis( L ) );;
gap> K:= LieCentralizer( L, Subalgebra( L, [ b[61]+b[79]+b[101]+b[102] ] ) );
<Lie algebra of dimension 102 over Rationals>
gap> lev:= LeviMalcevDecomposition(K);;
gap> SemiSimpleType( lev[1] );
"B3 A1"
   
  I need to find "F4 G2" and "D4 D4" types in E8. Any suggestions or references
where the particular example in the docs came from would be very helpful.
   
  Thanks,
   
  R.N.

       
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