The algebraic homomorphism of groups of Lie type over the ring k corresponding to the root datum morphism φ. See Chapter GROUPS OF LIE TYPE.
> RGL := StandardRootDatum( "A", 3 ); > RPGL := RootDatum( "A3" ); > A := VerticalJoin( SimpleRoots(RGL), Vector([Rationals()|1,1,1,1]) )^-1 * > VerticalJoin( SimpleRoots(RPGL), Vector([Rationals()|0,0,0]) ); > B := VerticalJoin( SimpleCoroots(RGL), Vector([Rationals()|1,1,1,1]) )^-1 * > VerticalJoin( SimpleCoroots(RPGL), Vector([Rationals()|0,0,0]) ); > phi := GroupOfLieTypeHomomorphism( hom< RGL -> RPGL | A, B >, Rationals() ); > GL := Domain( phi ); > phi( elt<GL|<1,2>, Vector([Rationals()| 7,1,11,1])> ); x1(2) ( 7 1/11 11)