[GAP Forum] Algebras

[Andrew Langworthy (MTH)]

Dear Forum,

I am trying to define algebra maps between a free associative algebra with a one on n generators (modulo some relations), and itself. I am using the command "AlgebraGeneralMappingByImages", but keep getting errors, specifically the "no method found" one. (same thing happens for AlgebraWithOneGeneralMappingByImages)

I have tried various "with/without one" combinations without success. I know that some of the algebra maps are not yet implemented in GAP (at least that is what it tells me when I try an use the command AlgebraHomomorphismByImages), but I cannot seem to get anywhere.

Am I making some silly mistake?

Thanks,
Andrew



In case anyone wants it, here is my code

rewrite:=FreeAssociativeAlgebraWithOne(Rationals,n,"s");

genalg:=GeneratorsOfAlgebra(rewrite);
rels1:=[];

for i in [1..n] do
    AddSet(rels1,genalg[i]^2-genalg[i]);

    for j in [1..n] do
        AddSet(rels1,genalg[i]*genalg[j]-genalg[j]*genalg[i]);
    od;
od;

RLalg:=rewrite/rels1;

s:=GeneratorsOfAlgebra(RLalg);




                #EPSILON IN RLalg


imep:=[1..n+1];

for i in [1..n+1] do
    imep[i]:=(0)*s[1];
od;

for i in [2..n+1] do
    imep[1]:=imep[1]+s[i]; #Defines imep1

    for j in [2..n+1] do
        imep[i]:=imep[i]+s[i]*s[j];
    od;

    imep[i]:=imep[i]-s[i]*s[i]; #removes the duplicates
od;


epsilon:=AlgebraGeneralMappingByImages(RLalg,RLalg,s,imep);