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Fix Embedding of a family into its LieFamily #6784

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Fix Embedding of a family into its LieFamily #6784

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20 changes: 13 additions & 7 deletions lib/liefam.gi
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Original file line number Diff line number Diff line change
Expand Up @@ -422,7 +422,7 @@ InstallOtherMethod( Embedding,
fi;

# Make the mapping object.
emb := Objectify( TypeOfDefaultGeneralMapping( Fam, LieFam,
emb := Objectify( NewType( GeneralMappingsFamily( Fam, LieFam ),
IsLieEmbeddingRep
and IsNonSPGeneralMapping
and IsMapping
Expand Down Expand Up @@ -455,18 +455,24 @@ InstallMethod( PreImagesElmNC,
return [ elm![1] ];
end );

# The embedding is a bijection of families, so every element of the
# range family has a preimage, and there is no range domain to test.
InstallMethod( PreImagesElm,
"for Lie embedding and Lie object in default representation",
FamRangeEqFamElm,
[ IsGeneralMapping and IsLieEmbeddingRep,
IsLieObject and IsPackedElementDefaultRep ], 0,
function( emb, elm )
if not ( elm in Range(emb) ) then
Error( "<elm> is not in the range of mapping <emb>" );
elif not ( elm in Image(emb) ) then
return [];
fi;
return PreImagesElmNC( emb, elm );
return [ elm![1] ];
end );

InstallMethod( PreImagesRepresentative,
"for Lie embedding and Lie object in default representation",
FamRangeEqFamElm,
[ IsGeneralMapping and IsLieEmbeddingRep,
IsLieObject and IsPackedElementDefaultRep ], 0,
function( emb, elm )
return elm![1];
end );

#############################################################################
Expand Down
15 changes: 15 additions & 0 deletions tst/testbugfix/2026-10-23-LieFamily-Embedding.tst
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Original file line number Diff line number Diff line change
@@ -0,0 +1,15 @@
# Embedding( Fam, LieFamily( Fam ) ) used to fail with a no method error
gap> F := FamilyObj( 1 );; L := LieFamily( F );;
gap> emb := Embedding( F, L );;
gap> 3 ^ emb = LieObject( 3 );
true
gap> PreImagesRepresentative( emb, LieObject( 3 ) );
3
gap> PreImagesElm( emb, LieObject( 3 ) );
[ 3 ]
gap> m := [ [ 1, 2 ], [ 3, 4 ] ];;
gap> F := FamilyObj( m );; emb := Embedding( F, LieFamily( F ) );;
gap> m ^ emb = LieObject( m );
true
gap> PreImagesRepresentative( emb, LieObject( m ) ) = m;
true
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