[GAP Forum] Algebras
Andrew Langworthy (MTH)
A.Langworthy at uea.ac.uk
Mon Jan 27 13:46:33 GMT 2014
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);
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