https://github.com/mtrunkat/diploma-algorithms-in-representation-theory
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.
https://github.com/mtrunkat/diploma-algorithms-in-representation-theory
algebra almost-split-sequences gap qpa representation-theory
Last synced: 2 months ago
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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.
- Host: GitHub
- URL: https://github.com/mtrunkat/diploma-algorithms-in-representation-theory
- Owner: mtrunkat
- Created: 2020-01-02T20:20:04.000Z (over 5 years ago)
- Default Branch: master
- Last Pushed: 2020-03-27T19:07:14.000Z (about 5 years ago)
- Last Synced: 2025-01-04T23:24:22.521Z (4 months ago)
- Topics: algebra, almost-split-sequences, gap, qpa, representation-theory
- Language: TeX
- Homepage:
- Size: 1.03 MB
- Stars: 1
- Watchers: 2
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# Algorithms in Representation Theory
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
## How to run
### Prerequisites
1. Install **GAP** following this tutorial [http://www.gap-system.org/Download/index.html](http://www.gap-system.org/Download/index.html)
2. Install **QPA** package pas described at [http://www.math.ntnu.no/~oyvinso/QPA/](http://www.math.ntnu.no/~oyvinso/QPA/)
### Execution
1. Run **GAP**
2. Load **QPA** package via `LoadPackage("QPA");`
3. Copy whole `src/code/algorithm.g` to command line to register `AlmostSplitSequence2` function along with other helper functions.
4. 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]);
```