This thesis deals with implementation of algorithm for computation of generator of almost split sequences ending at an indecomposable nonprojective module of path algebra over finite quiver. Algorithm is implemented in algebra system GAP (Groups, Algorithms, Programming) with additional package QPA (Quivers and Path Algebras).
Department of Algebra, Faculty of Mathematics and Physics, Charles University
Author: Marek Trunkát, Supervisor: RNDr. Jan Šťovíček, Ph.D., Department of Algebra
- Install GAP following this tutorial http://www.gap-system.org/Download/index.html
- Install QPA package pas described at http://www.math.ntnu.no/~oyvinso/QPA/
- Run GAP
- Load QPA package via
LoadPackage("QPA");
- Copy whole
src/code/algorithm.g
to command line to registerAlmostSplitSequence2
function along with other helper functions. - Now you can use this function to compute a generator of
DTr(X) → E → X
:
K := Rationals;
Q := Quiver(3, [[1, 2, "a"], [2, 3, "b"],[1, 3, "c"]]);
KQ := PathAlgebra(K,Q);
A := KQ;
matrices := [ ["a", [[1,0,0],[0,1,0]]],
["b", [[0,1],[1,0],[0,1]]],
["c", [[0,0],[1,0]]] ];
mX := RightModuleOverPathAlgebra(A,matrices);
E := AlmostSplitSequence2( mX );
To compute just an E module add following line:
E := Range(E[1]);