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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