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8 Algebras and their homomorphisms
 8.1 Homomorphisms by function

8 Algebras and their homomorphisms

8.1 Homomorphisms by function

8.1-1 AlgebraHomomorphismByFunction
‣ AlgebraHomomorphismByFunction( A, B, f )( operation )
‣ AlgebraWithOneHomomorphismByFunction( A, B, f )( operation )

Returns: A homomorphism from the algebra A to the algebra B.

These functions have been transferred from package FR. The first was also transferred from the package XModAlg.

These functions construct an algebra homomorphism from a one-argument function. They do not check that the function actually defines a homomorphism.


gap> A := MatrixAlgebra( Rationals, 2 );
( Rationals^[ 2, 2 ] )
gap> e1 := AlgebraHomomorphismByFunction( Rationals, A, f -> [[f,0],[0,0]] );
MappingByFunction( Rationals, ( Rationals^[ 2, 2 ] ), function( f ) ... end )
gap> 11^e1;
[ [ 11, 0 ], [ 0, 0 ] ]

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