Here we present some code for the GAP package QPA (https://oyvinso.folk.ntnu.no/QPA/) that was used in some of my articles.
Contracted preprojective algebras (https://arxiv.org/abs/2409.05603). Let A=KQ/I be a preprojective algebra of Dynkin type and e an idempotent given as the sum of primitive idempotents corresponding to the vertices of A. A contracted preprojective algebra of Dynkin type is an algebra Morita equivalent to eAe. For the proof of Theorem 4.6(4) of the article https://arxiv.org/abs/2409.05603 the homological dimension idim B, gldim B and domdim B can be calculated using QPA when B is a contracted preprojective algebra of Dynkin type E_6. The following text-file shows how to use QPA to obtain explicit quiver and relations of contracted preprojective algebras:
The following QPA-code tests whether a given connected quiver algebra KQ/I is representation-finite and outputs the number of indecomposable modules together with a list of all indecomposable modules in case the algebra is representation-finite. It currently only works over finite fields. What is needed to make it work in general is a code that can decompose modules over infinite fields. The program was developed together with Bernhard Böhmler and used in experiments and several articles: