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Identifier
Values
=>
Cc0005;cc-rep
[1,0,1,0]=>2 [1,0,1,0,1,0]=>3 [1,0,1,1,0,0]=>2 [1,1,0,0,1,0]=>2 [1,1,0,1,0,0]=>2 [1,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,1,0,0]=>3 [1,0,1,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,0]=>3 [1,0,1,1,1,0,0,0]=>2 [1,1,0,0,1,0,1,0]=>3 [1,1,0,0,1,1,0,0]=>2 [1,1,0,1,0,0,1,0]=>3 [1,1,0,1,0,1,0,0]=>3 [1,1,0,1,1,0,0,0]=>2 [1,1,1,0,0,0,1,0]=>2 [1,1,1,0,0,1,0,0]=>2 [1,1,1,0,1,0,0,0]=>2 [1,0,1,0,1,0,1,0,1,0]=>3 [1,0,1,0,1,0,1,1,0,0]=>3 [1,0,1,0,1,1,0,0,1,0]=>3 [1,0,1,0,1,1,0,1,0,0]=>3 [1,0,1,0,1,1,1,0,0,0]=>3 [1,0,1,1,0,0,1,0,1,0]=>3 [1,0,1,1,0,0,1,1,0,0]=>3 [1,0,1,1,0,1,0,0,1,0]=>3 [1,0,1,1,0,1,0,1,0,0]=>4 [1,0,1,1,0,1,1,0,0,0]=>3 [1,0,1,1,1,0,0,0,1,0]=>3 [1,0,1,1,1,0,0,1,0,0]=>3 [1,0,1,1,1,0,1,0,0,0]=>3 [1,0,1,1,1,1,0,0,0,0]=>2 [1,1,0,0,1,0,1,0,1,0]=>3 [1,1,0,0,1,0,1,1,0,0]=>3 [1,1,0,0,1,1,0,0,1,0]=>3 [1,1,0,0,1,1,0,1,0,0]=>3 [1,1,0,0,1,1,1,0,0,0]=>2 [1,1,0,1,0,0,1,0,1,0]=>3 [1,1,0,1,0,0,1,1,0,0]=>3 [1,1,0,1,0,1,0,0,1,0]=>4 [1,1,0,1,0,1,0,1,0,0]=>4 [1,1,0,1,0,1,1,0,0,0]=>3 [1,1,0,1,1,0,0,0,1,0]=>3 [1,1,0,1,1,0,0,1,0,0]=>3 [1,1,0,1,1,0,1,0,0,0]=>3 [1,1,0,1,1,1,0,0,0,0]=>2 [1,1,1,0,0,0,1,0,1,0]=>3 [1,1,1,0,0,0,1,1,0,0]=>2 [1,1,1,0,0,1,0,0,1,0]=>3 [1,1,1,0,0,1,0,1,0,0]=>3 [1,1,1,0,0,1,1,0,0,0]=>2 [1,1,1,0,1,0,0,0,1,0]=>3 [1,1,1,0,1,0,0,1,0,0]=>3 [1,1,1,0,1,0,1,0,0,0]=>3 [1,1,1,0,1,1,0,0,0,0]=>2 [1,1,1,1,0,0,0,0,1,0]=>2 [1,1,1,1,0,0,0,1,0,0]=>2 [1,1,1,1,0,0,1,0,0,0]=>2 [1,1,1,1,0,1,0,0,0,0]=>2
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Description
The number of simple modules in $eAe$ with projective dimension at most 2 in the corresponding Nakayama algebra $A$ with minimal faithful projective-injective module $eA$.
Code
DeclareOperation("numbersimplesprojdimatmostkeAe",[IsList]);

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

local A,k,injA,RegA,temp,CoRegA,priA,U,UU,g,g2,B,T,TT,W,simB;

A:=LIST[1];
k:=LIST[2];
projA:=IndecProjectiveModules(A);priA:=DirectSumOfQPAModules(Filtered(projA,x->IsInjectiveModule(x)=true));
B:=EndOfModuleAsQuiverAlgebra(priA)[3];
simB:=SimpleModules(B);
W:=Filtered(simB,x->ProjDimensionOfModule(x,30)<=k);
return(Size(W));
end);

Created
May 14, 2018 at 11:30 by Rene Marczinzik
Updated
May 14, 2018 at 11:30 by Rene Marczinzik