[GAP Forum] AdjointBasis() and IndicesOfAdjointBasis()

[Kursat Aker]

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