"Source: Text/Algebra/AlgLie.text";
"Line: 790";
"Date: Thu Sep 25 14:47:46 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Algebra/AlgLie.text, line: 790
// Example: H110E10 ()
print "Example: H110E10";
ei := GetEchoInput();
SetEchoInput(true);
L<e,f> := FreeLieAlgebra(Rationals(), 2);
M := LieAlgebra("A1", Rationals() : Isogeny := "SC");
pos, neg, cart := ChevalleyBasis(M);
pos, neg, cart;
phi := hom<L -> M | [ pos[1], neg[1] ]>;
phi(e), phi(f), phi(e*f);
imgs := [ L | f, (f,e), e];
psi := map<M -> L | x :-> &+[ x[i]*imgs[i] : i in [1..3] ]>;
psi(cart[1]); 
psi(phi((e,(e,f))));
assert forall{b : b in Basis(M) | phi(psi(b)) eq b };
R := { x - psi(phi(x)) : x in {e, f, (e,f), (e,(e,f)), (f,(f,e))} };
L2 := quo<L | R>;
L2;
SemisimpleType(L2);
SetEchoInput(ei);
