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products/Sources/formale Sprachen/GAP/pkg/qpa/doc/ (Algebra von RWTH Aachen Version 4.15.1^©) Datei vom 4.0.2024 mit Größe 6 kB

Quellcode-Bibliothek qpadocumentation.xml Sprache: XML

<?xml version="1.0" encoding="UTF-8"?>



<!DOCTYPE Book SYSTEM "gapdoc.dtd">
</Alt>'>
]> -->

<?LaTeX ExtraPreamble="
\usepackage{amsmath}
\usepackage[all]{xy}
\newcommand{\tensor}{\otimes}
\newcommand{\quiverproduct}{\times}
\newcommand{\add}{\operatorname{add}\nolimits}
\newcommand{\Hom}{\operatorname{Hom}\nolimits}
\newcommand{\End}{\operatorname{End}\nolimits}
\newcommand{\Ext}{\operatorname{Ext}\nolimits}
\newcommand{\rad}{\operatorname{rad}\nolimits}
\newcommand{\op}{{\operatorname{op}\nolimits}}
\renewcommand{\Im}{\operatorname{Im}\nolimits}
\DeclareMathOperator{\modc}{mod}
\DeclareMathOperator{\proj}{proj}
"?>

<Book Name="QPA">

<TitlePage>
  <Title>QPA</Title>
  <Subtitle>Quivers and Path Algebras</Subtitle>
  <Version>Version <#Include SYSTEM "../version"></Version>
  <TitleComment>
  </TitleComment>
  <Author>The QPA-team
          <Email>oyvind.solberg@ntnu.no</Email>
       <Homepage>https://folk.ntnu.no/oyvinso/QPA/</Homepage>
          <Address>
            Department of Mathematical Sciences<Br/>
            NTNU<Br/>
            N-7491 Trondheim<Br/>
            Norway
          </Address>
  </Author>

  <Date>January 2024</Date>

  <Abstract>
    The GAP4 deposited package <Package>QPA</Package> extends the
    GAP functionality for computations with finite dimensional
    quotients of path algebras. <Package>QPA</Package> 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 constructing 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.
  </Abstract>
  <Copyright>©right; 2014-2024 by The QPA-team.<P/>

  <Package>QPA</Package> 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
  (<URL>https://www.gnu.org/licenses/gpl.html</URL>).<P/>

  If you obtained <Package>QPA</Package>, 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
  <Package>QPA</Package>, please cite it in the following form:<P/>

  The QPA-team, <Package>QPA</Package> - Quivers, path algebras and
  representations, Version <#Include SYSTEM "../version">; 2024
  (<URL>https://folk.ntnu.no/oyvinso/QPA/</URL>)
  </Copyright>

  <Acknowledgements>The system design of <Package>QPA</Package> 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:

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

</TitlePage>

<TableOfContents/>

<Body>

<#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">

</Body>



<Bibliography Databases="qpadocumentation.bib" />

<TheIndex/>

</Book>

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