40.6 Algebra Functions for Matrix Algebras

Centralizer( A, a )

Centralizer( A, S ) :

returns the element or subalgebra centralizer in the matrix algebra A. Centralizers in matrix algebras are computed by solving a linear equation system.

Centre( A ) :

returns the centre of the matrix algebra A, which is computed by solving a linear equation system.

FpAlgebra( A ) :

returns a finitely presented algebra that is isomorphic to A. The presentation is computed using the structure constants, thus a vector space basis of A has to be computed. Zero and One for Matrix Algebras) an error is signalled. (At the moment the implementation is really simpleminded.)

    gap> a:= UnitalAlgebra( Rationals, [[[0,1],[0,0]]] );
    UnitalAlgebra( Rationals, [ [ [ 0, 1 ], [ 0, 0 ] ] ] )
    gap> FpAlgebra( a );
    UnitalAlgebra( Rationals, [ a.1 ] )
    gap> last.relators;
    [ a.1^2 ] 

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