38.23 OperationHomomorphism for Algebras

OperationHomomorphism( A, B )

returns the algebra homomorphism (see Algebra Homomorphisms) with source A and range B, provided that B is a matrix algebra that was constructed as operation of A on a suitable module M using Operation( A, M ), see Operation for Algebras.

    gap> ophom:= OperationHomomorphism( a, op );
    OperationHomomorphism( UnitalAlgebra( Rationals,
    [ [ [ 1, 0 ], [ 0, 0 ] ] ] ), UnitalAlgebra( Rationals,
    [ [ [ 1 ] ] ] ) )
    gap> Image( ophom, a.1 );
    [ [ 1 ] ]
    gap> Image( ophom, Zero( a ) );
    [ [ 0 ] ]
    gap> PreImagesRepresentative( ophom, [ [ 2 ] ] );
    [ [ 2, 0 ], [ 0, 2 ] ] 

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