[GAP Forum] Constructing bilinear maps for matrix multiplication

[Lisette Brillemans]

Hi!

> 2. Also, I don't understand the behaviour of the 
> 
> IsAlgebraWithOne( algebra )
> 
> function.  For example, I have defined
> 
> gap> A := FullMatrixAlgebra( Rationals, 3 );
> ( Rationals^[ 3, 3 ] )
> 
> This is an algebra with One( A ) = [ [1,0,0], [0,1,0], [0,0,1]].  However,
> when I construct the direct S = sum A \otimes A by
> 
> gap> S := DirectSumOfAlgebras( A, A );
> <algebra over Rationals, with 6 generators>
> 
> This has the unit
> 
> gap> One( S );
> [ [ 1, 0, 0, 0, 0, 0 ], [ 0, 1, 0, 0, 0, 0 ], [ 0, 0, 1, 0, 0, 0 ], [ 0, 0, 0, 1, 0, 0 ], [ 0, 0, 0, 0, 1, 0 ], 
>  [ 0, 0, 0, 0, 0, 1 ] ]
> 
> however, IsAlgebraWithOne( S ) is returning false:
> 
> gap> IsAlgebraWithOne( S );
> false
> 
> Sincerely, Sandeep.

It's just this kind of things that surpise me as well. In one of my
earlier posts a few days ago I stated that 

ListX(Combinations(a,2),Combinations(a,2),\>,pair); works but

ListX(Combinations(a,2),Combinations(a,2),\<,pair); doesn't.

(of course a and pair are defined separately)

Which is unlogical as well.

Your IsAlgebraWithOne(S); should be true of course. 

Gap isn't perfect.


Sincerely,


Lisette