Quivers and path algebras

The aim

The "Quivers and Path Algebras" team has as a goal to develop a GAP package(s) for carrying out computations for finite dimensional quotients of path algebras over the fields that are available in GAP. The package we aim to develop for GAP is called QPA for Quivers and Path Algebras.

A bit of history

The system design of QPA was initiated by Edward L. Green, Lenwood S. Heath, and Craig A. Struble. It was continued and completed by Randall Cone and Edward Green. In addition, the following persons have given valuable contributions: Nicholas Allen (orderings, tensor products, user documentation), Gerard Brunick (quivers, path algebras, Drinfeld double), Timothy Terriberry (orderings) and George Yuhasz (user documentation, matrix representations of path algebras, tensor products).

What is it?

The current version of the QPA package have the basic features for creating a program that can do a variety of computations for finite dimensional qoutients of path algebras. In particular, it has data structures for quivers, quotients of path algebras, and representations of quivers with relations. One of the major aims is to be able to contruct projective resolutions of finitely generated modules over finite dimensional quotients of path algebras. This is not yet available.

In addition to the above, we have a long list of computations we want to implement in our package, see the

If you have suggestions of computations/algorithms that you want to see implemented and it is not on the list, please contact us.

What can it do?

Here is what you can do in the latest version (or at least hopefully modulo bugs) of QPA,

Downloading/installing and contributing

For intalling and downloading: Assuming that GAP is installed on your comupter, follow the following steps:

1. Make a directory, say GAPdirectory.
2. In the GAPdirectory, create a subdirectory gap, with again a subdirectory pkg, that is, now you should have a directory GAPdirectory/gap/pkg/.
3. Move to the directory GAPdirectory/gap/pkg/
4. Give the following two commands (press "return" when asked for a password):
   • cvs -d:pserver:anonymous@quiverspathalg.cvs.sourceforge.net:/cvsroot/quiverspathalg login
   • cvs -z3 -d:pserver:anonymous@quiverspathalg.cvs.sourceforge.net:/cvsroot/quiverspathalg co -P qpa
5. QPA is using the GAP-package GBNP, go to this webpage and download the latest version of this package. Unpack it in the directory GAPdirectory/gap/pkg/.
6. The directory GAPdirectory/gap/pkg/ should now have two subdirectories, gbnp and qpa.
7. When starting GAP, use the command: gap -l ";/fullpath/GAPdirectory/gap/", where "fullpath" is the complete directory path name for the directory containing the subdirectory GAPdirectory. Or for convenience, define an alias, for instance in .bashrc, alias gap='gap -l ";/fullpath/GAPdirectory/gap/"'.
8. Making the documentation: To compile the documentation, one needs the GAP-package, GAPDoc. Download and install this as GBNP and QPA, ie. in the GAPdirectory/gap/pkg/-directory.
   1. Move to the directory GAPdirectory/gap/pkg/qpa/doc
   2. Give the command: gap MakeQPADoc.gi
   3. The above will start gap, and it will leave you inside a GAP-session. Type exit, to exit.
   4. You now find a file called manual.pdf in the directory GAPdirectory/gap/pkg/qpa/doc. This is the manual for QPA.

The QPA-team

The current group of people contributing to this project is: