38.5 UnitalAlgebra

UnitalAlgebra( U )

returns a unital parent algebra A which is isomorphic to the parent algebra or subalgebra U. If U is not unital it is checked whether the zero-th power of elements is contained in U, and if not an error is signalled.

UnitalAlgebra( F, gens )
UnitalAlgebra( F, gens, zero )

returns a unital 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> alg1:= UnitalAlgebra( Rationals, [ NullMat( 2, 2 ) ] );
    UnitalAlgebra( Rationals, [ [ [ 0, 0 ], [ 0, 0 ] ] ] )
    gap> alg2:= UnitalAlgebra( Rationals, [], NullMat( 2, 2 ) );
    UnitalAlgebra( Rationals, [ [ [ 0, 0 ], [ 0, 0 ] ] ] )
    gap> alg3:= Algebra( alg1 );
    Algebra( Rationals, [ [ [ 0, 0 ], [ 0, 0 ] ], [ [ 1, 0 ], [ 0, 1 ] ]
     ] )
    gap> alg1 = alg3;
    true
    gap> AsUnitalAlgebra( alg3 );
    UnitalAlgebra( Rationals,
    [ [ [ 0, 0 ], [ 0, 0 ] ], [ [ 1, 0 ], [ 0, 1 ] ] ] ) 

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

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