<!-- Id: manual.xml,v 1.2 2006/09/29 11:49:53 gap Exp  -->
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<!DOCTYPE Book SYSTEM "gapdoc.dtd"
[<!ENTITY LieAlgDB "<Package>LieAlgDB</Package>">] >

<Book Name="LieAlgDB">

<TitlePage>
  <Title>&LieAlgDB;</Title>
  <Subtitle>A database of Lie algebras</Subtitle>
  <Version>Version 2.0.2</Version>

<Author>
  Willem de Graaf
  <Email>degraaf@science.unitn.it</Email>
  <Homepage>http://www.science.unitn.it/~degraaf/</Homepage>
          <Address>
    	    Dipartimento di Matematica<Br/>
Via Sommarive 14<Br/>
I-38050 Povo (Trento)<Br/>
Italy<Br/>
       </Address> 
  </Author>

  <Author>
  Csaba Schneider
  <Email>csaba.schneider@sztaki.hu</Email>
  <Homepage>http://www.sztaki.hu/~schneider</Homepage>
          <Address>
    	    Informatics Research Laboratory<Br/>
    	    Computer and Automation Research Institute<Br/>
    	    1518 Budapest Pf. 63.<Br/>
    	    Hungary
       </Address> 
  </Author>

  <Date>September 2007</Date>



<Abstract>
This package provides access to the classification of the following 
families of Lie algebras:
<List>
<Item> non-solvable Lie algebras over finite fields up to dimension 6;
</Item>
<Item> nilpotent Lie algebras of dimension up to 9 over <A>GF(2)</A>, of dimension
up to 7 over <A>GF(3)</A> or <A>GF(5)</A>;</Item>
<Item> simple Lie algebras of dimensions between 7 and 9 over <A>GF(2)</A>;
</Item>
<Item> the classification of solvable Lie algebras of dimension at most 4;
</Item>
<Item> the classification of nilpotent Lie algebras of dimensions at most 5
and those of dimension 6 over fields  of odd characteristic.
</Item>
</List>
</Abstract>

<Copyright>
  &copyright; 2006--2007 Willem de Graaf and Csaba Schneider
</Copyright>
  
<Acknowledgements>
We are grateful to Andrea Caranti, Marco Costantini, Bettina Eick, 
Helmut Strade, Michael Vaughan-Lee. Without 
their help, interest, and encouragement, this package would not have been 
completed. We also acknowledge the effort of the referees to improve the
implementation and the documentation.
</Acknowledgements>

</TitlePage>

<TableOfContents/>

<Body>

<Chapter> <Heading>Introduction</Heading>

This is the manual for the &GAP; package <Package>LieAlgDB</Package>, 
for accessing and working with several classifications of Lie algebras. <P/>
In the mathematical literature many classifications of Lie algebras of various
types have been published (we refer to the bibliography for a few examples). 
However, working with these classifications from paper is not always easy.
This package aims at making a few classifications of small-dimensional Lie
algebras that have appeared in recent years more accessible. For each 
classification that is contained in the package,
functions are provided that construct Lie algebras from that classification
inside &GAP;. This allows the user to obtain easy access to the often rather
complicated data contained in a classification, and to directly interface
the Lie algebras to the functionality for Lie algebras which is already
contained in the system. <P/>
The package contains the following classifications:
<List>
<Item> non-solvable Lie algebras over finite fields up to dimension 6 (from <Cite Key="Strade"/>);
</Item>
<Item> nilpotent Lie algebras of dimension up to 9 over <A>GF(2)</A>, of dimension
up to 7 over <A>GF(3)</A> or <A>GF(5)</A> (from <Cite Key="sch"/>);</Item>
<Item> simple Lie algebras of dimensions between 7 and 9 over <A>GF(2)</A> (from <Cite Key="VL"/>);
</Item>
<Item> the classification of solvable Lie algebras of dimension at most 4 (from <Cite Key="wdg05"/>); 
</Item>
<Item> the classification of nilpotent Lie algebras of dimension at most 
5 and those
of dimension 6 whose underlying field does not have characteristic 2 (from <Cite Key="wdg07"/>).
</Item>
</List>

This manual is structured as follows. The next chapter contains a description of the main
functions of the package. The third chapter contains descriptions of the
classifications used in the package. These are of course also contained in published papers,
but for the convenience of the user they have been added here.


</Chapter>


<#Include SYSTEM "families.xml">

<Chapter><Heading>A description of the Lie algebras that are contained in the package</Heading>

<#Include SYSTEM "appnonsolv.xml">
<#Include SYSTEM "appsimple.xml">
<#Include SYSTEM "appsolv.xml">


</Chapter>
</Body>

<Bibliography Databases="manual"/>

</Book>
