Problems with PreprojectiveAlgebra

[Nakayamaalgebra]

Here is a program used in the following to get all indecomposable modules for a Dynkin type path algebra:

DeclareOperation("allindecomposablesdynkin",[IsList]);

InstallMethod(allindecomposablesdynkin, "for a representation of a quiver", [IsList],0,function(LIST)

local A,C,n,injA,W,i,WW,l;

A:=LIST[1]; C:=CoxeterMatrix(A); n:=Order(C); injA:=IndecInjectiveModules(A); W:=[];for i in injA do for l in [0..n] do Append(W,[DTr(i,l)]);od;od; WW:=Filtered(W,x->Dimension(x)>0); return(WW);

end);

Here are two errors related to the program PreprojectiveAlgebra:

Q:=DynkinQuiver("A",3,["r","l"]);A:=PathAlgebra(GF(3),Q);C:=CoxeterMatrix(A);n:=Order(C);L:=allindecomposablesdynkin([A]);Size(L);M:=DirectSumOfQPAModules(L);B:=PreprojectiveAlgebra(M,n);

Error, no method found! For debugging hints type ?Recovery from NoMethodFound Error, no 3rd choice method found for `RadicalOfAlgebra' on 1 arguments called from RadicalOfAlgebra( A ) at /home/Schreibtisch/gap4r8/pkg/qpa/lib/algebra.gi:681 called from AlgebraAsQuiverAlgebra( A ) at stdin:21675 called from <function "unknown">( ) called from read-eval loop at line 21717 of stdin you can 'quit;' to quit to outer loop, or you can 'return;' to continue brk> quit;

Another error:

Q:=DynkinQuiver("A",3,["r","r"]);A:=PathAlgebra(GF(3),Q);C:=CoxeterMatrix(A);n:=Order(C);L:=allindecomposablesdynkin([A]);Size(L);M:=DirectSumOfQPAModules(L);B:=PreprojectiveAlgebra(M,n);

Error, entered map is not a module map between the representations entered, error for vertex number 1 and arrow a_1, called from RightModuleHomOverAlgebra( B, C, h!.maps ) at /home/Schreibtisch/gap4r8/pkg/qpa/lib/functors.gi:825 called from TrD( g ) at stdin:9382 called from TrD( q, i - 1 ) at stdin:21652 called from <function "unknown">( ) called from read-eval loop at line 21717 of stdin you can 'quit;' to quit to outer loop, or you can 'return;' to continue

[sunnyquiver]

I have added a new version of PreprojectiveAlgebra of a finite dimensional hereditary algera given as a path algebra of a quiver. This is using the description of the preprojective algebra of a hereditary algebra by Gelfand-Panomarev by the double quiver and mesh relations.

[Nakayamaalgebra]

Thanks. The program PreprojectiveAlgebra was a program for any module M over KQ (so the output might be some new algebras) before and now it only gives the classical preprojective algebras asociated to Q if I undertand correctly.

[sunnyquiver]

The old version of PreprojectiveAlgebra has been modified, and now it will hopefully work. Please test it and tell me if it needs more work.

[Nakayamaalgebra]

Thank you very much! I have not yet updated QPA but read into QPA the two modified programs you made. It seems to work now in more examples but there is still an error it seems: Q:=DynkinQuiver("D",4,["r","r","r"]);A:=PathAlgebra(GF(3),Q);L:=IndModDynkin([A]);M:=DirectSumOfQPAModules(L);B:=PreprojectiveAlgebra(M,44); Error, codomain of the first argument is not equal to the domain of the second argument, called from f * gpowers at *stdin*:21524 called from <function "unknown">( <arguments> ) called from read-eval loop at line 21582 of *stdin* you can 'quit;' to quit to outer loop, or you can 'return;' to continue

Here the needed program to input this (it calculates all indecomposables for dynkin type path algebras)

DeclareOperation("IndModDynkin",[IsList]);

InstallMethod(IndModDynkin, "for a Dynkin path algebra", [IsList],0,function(LIST)

local A,C,n,injA,W,i,WW,l;

A:=LIST[1];
C:=CoxeterMatrix(A);
n:=Order(C);
injA:=IndecInjectiveModules(A);
W:=[];for i in injA do for l in [0..n] do Append(W,[DTr(i,l)]);od;od;
WW:=Filtered(W,x->Dimension(x)>0);
return(WW);

end);