Dear GAP Forum,
I now understood that the answer to my question is yes.
My confusion was a result of me looking at
gap> Elements(B);
[k, j, i, e]
I should have look at
gap> BasisVectors(B);
[e,i,j,k]
Sorry for bothering the Forum.
Best wishes,
Kursat
On 6/22/10 8:37 PM, Kursat Aker wrote:
Dear GAP Forum,
I would like to ask a question about AdjointBasis().
I have the following code, which I essentially took from GAP Manual.
gap> A:= QuaternionAlgebra( Rationals );;
gap> B := Basis( A );
Basis( <algebra-with-one of dimension 4 over Rationals>, ... )
gap> Elements( B );
[ k, j, i, e ]
gap> adjB := AdjointBasis( B );
Basis( <vector space over Rationals, with 4 generators>,
[ [ [ 1, 0, 0, 0 ], [ 0, 1, 0, 0 ], [ 0, 0, 1, 0 ], [ 0, 0, 0, 1 ] ],
[ [ 0, -1, 0, 0 ], [ 1, 0, 0, 0 ], [ 0, 0, 0, -1 ], [ 0, 0, 1, 0 ] ],
[ [ 0, 0, -1, 0 ], [ 0, 0, 0, 1 ], [ 1, 0, 0, 0 ], [ 0, -1, 0, 0 ] ],
[ [ 0, 0, 0, -1 ], [ 0, 0, -1, 0 ], [ 0, 1, 0, 0 ], [ 1, 0, 0, 0 ] ]
] )
gap> IndicesOfAdjointBasis( adjB );
[ 1, 2, 3, 4 ]
My question is this:
Is the matrix adjB[i] supposed to the left action of the element B[i]
for i=1,2,3,4?
Thanks,
Kursat
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