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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 1.0</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>October 2006</Date>



<Abstract>
This package provides access to the the classification of the following 
families of Lie algebras:
<List>
<Item>solvable Lie algebras of dimension at most 4;
</Item>
<Item>nilpotent Lie algebras of dimension at most 5, and those 
of dimension~6 over a field of characteristic different from 2;
</Item>
<Item>
non-solvable Lie algebras of dimension at most 6 over finite fields;
</Item>
<Item>
simple Lie algebras of dimension at most 6 over finite fields and those of
dimension at most 9 over <A>GF(2)</A>.
</Item>
</List>
</Abstract>

<Copyright>
  &copyright; 2006 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.
</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 mathematics 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 &GAP;. <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 upto 9 over <A>F=GF(2)</A>, of dimension
upto 7 over <A>F=GF(3)</A> or <A>F=GF(5)</A> (from <Cite Key="sch"/>),</Item>
<Item> simple Lie algebras of dimensions between 7 and 9 over <A>F=GF(2)</A> (from <Cite Key="VL"/>),
</Item>
<Item> the classification of solvable Lie algebras of dimensions 2,3, and 4 (from <Cite Key="wdg05"/>), 
</Item>
<Item> the classification of nilpotent Lie algebras of dimensions 5 and 6 (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. Subsequently, the appendices contain 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>


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</Body>

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<Bibliography Databases="manual"/>

</Book>
