38.4 Algebra

Algebra( U )

returns a parent algebra A which is isomorphic to the parent algebra or subalgebra U.

Algebra( F, gens )
Algebra( F, gens, zero )

returns a parent algebra over the field F and generated by the algebra elements in the list gens. The zero element of this algebra may be entered as zero; this is necessary whenever gens is empty.

    gap> a:= [ [ 1 ] ];;
    gap> alg:= Algebra( Rationals, [ a ] );
    Algebra( Rationals, [ [ [ 1 ] ] ] )
    gap> alg.name:= "alg";;
    gap> sub:= Subalgebra( alg, [] );
    Subalgebra( alg, [  ] )
    gap> Algebra( sub );
    Algebra( Rationals, [ [ [ 0 ] ] ] )
    gap> Algebra( Rationals, [], 0*a );
    Algebra( Rationals, [ [ [ 0 ] ] ] ) 

The algebras returned by Algebra are not unital. For constructing unital algebras, use UnitalAlgebra UnitalAlgebra.

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