[GAP Forum] a problem with matrix algebras and homomorphisms

Laurent Bartholdi laurent.bartholdi at epfl.ch
Thu Oct 28 17:48:19 BST 2004

i'm trying to set up the following:

A := FreeAssociativeAlgebraWithOne(Integers,"s","f");
s := A.1; f := A.2; z := Zero(A); o := One(A);
M := MatrixAlgebra(A,2);
phi := AlgebraHomomorphismByImages(A,M,[s,f],[[[z,o],[o,z]],[[f,z],[s,z]]]);

i.e. a free associative algebra A, and a map phi from A to 2x2 matrices
over itself.

unfortunately, gap chokes saying
Error, <S> and <R> must have same left acting domain called from ...

now on one side it's true that they don't have the same acting domain; all
that's needed is that <R> _contain_ the left acting domain of <S>.
so i tried to double-think gap with "M!.LeftActingDomain := Integers",
but then i get in to the error that the matrix entries are not in

thanks for your help,

Laurent Bartholdi           \  laurent.bartholdi<at>epfl<dot>ch
EPFL, IGAT, Bâtiment BCH     \    Téléphone: +41 21-6930380
CH-1015 Lausanne, Switzerland \      Fax: +41 21-6930385

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