## QPA

Quivers and Path Algebras
Version <#Include SYSTEM "../version">
The QPA-team oyvind.solberg@math.ntnu.no http://www.math.ntnu.no/~oyvinso/QPA/

                Department of Mathematical Sciences

                NTNU

                N-7491 Trondheim

                Norway

October 2016

The GAP4 deposited package `QPA` extends the GAP functionality for computations with finite dimensional quotients of path algebras. `QPA` has data structures for quivers, quotients of path algebras, representations of quivers with relations and complexes of modules. Basic operations on representations of quivers are implemented as well as contructing minimal projective resolutions of modules (using using linear algebra). A not necessarily minimal projective resolution constructed by using Groebner basis theory and a paper by Green-Solberg-Zacharia, "Minimal projective resolutions", has been implemented. A goal is to have a test for finite representation type. This work has started, but there is a long way left. Part of this work is to implement/port the functionality and data structures that was available in CREP.

&copyright; 2010-2020 by The QPA-team.

QPA
is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. For details, see the FSF’s own site (http://www.gnu.org/licenses/gpl.html).

If you obtained `QPA`, we would be grateful for a short notification sent to one of members of the QPA-team. If you publish a result which was partially obtained with the usage of `QPA`, please cite it in the following form:

The QPA-team, `QPA` - Quivers, path algebras and representations, Version <#Include SYSTEM "../version">; 2016 (http://www.math.ntnu.no/~oyvinso/QPA/)
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. We would like to thank the following people for their contributions:

Chain complexes
Kristin Krogh Arnesen and Øystein Skartsæterhagen
Degeneration order for modules in finite type
Andrzej Mroz
GBNP interface (for Groebner bases)
Randall Cone
Homomorphisms of modules
Øyvind Solberg and Anette Wraalsen
Koszul duals
Stephen Corwin
Matrix representations of path algebras
Øyvind Solberg and George Yuhasz
Opposite algebra and tensor products of algebras
Øystein Skartsæterhagen
Predefined classes of algebras
Andrzej Mroz and Øyvind Solberg
Projective resolutions (using Groebnar basis)
Randall Cone and Øyvind Solberg
Projective resolutions (using linear algebra)
Øyvind Solberg
Quickstart
Kristin Krogh Arnesen
Quivers, path algebras
Gerard Brunick
The bounded derived category
Kristin Krogh Arnesen and Øystein Skartsæterhagen
Unitforms
Øyvind Solberg

<#Include SYSTEM "chapter_introduction.xml">

<#Include SYSTEM "chapter_quickstart.xml">

<#Include SYSTEM "chapter_quivers.xml">

<#Include SYSTEM "chapter_path_algebras.xml">

<#Include SYSTEM "chapter_groebner_bases.xml">

<#Include SYSTEM "chapter_right_modules.xml">

<#Include SYSTEM "chapter_homomorphisms.xml">

<#Include SYSTEM "chapter_homological_algebra.xml">

<#Include SYSTEM "chapter_AR-theory.xml">

<#Include SYSTEM "chapter_chain_complexes.xml">

<#Include SYSTEM "chapter_proj_and_derived.xml">

<#Include SYSTEM "chapter_combinatorialrep.xml">

<#Include SYSTEM "chapter_degorderfinitetype.xml">