"Source: Text/Algebra/AlgLie.text";
"Line: 4015";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgLie.text, line: 4015
// Example: H110E44 ()
print "Example: H110E44";
ei := GetEchoInput();
SetEchoInput(true);
L:=LieAlgebra("D3",RationalField());
L;
K:=sub< L | [L.1,L.2,L.3] >;
M:=Centralizer(L, K);
M;
R:=SolvableRadical(M);
R;
HasLeviSubalgebra(M);
K:=Centralizer(L, sub< L | [L.1,L.2,L.3] >);
K;
IsSolvable(K);
assert $1;
IsNilpotent(K);
assert $1;
R:= SolvableRadical(K);
IsSolvable(R);
assert $1;
IsNilpotent(R);
assert $1;
N:= Nilradical(K);
IsNilpotent(N);
assert $1;
SetEchoInput(ei);
