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<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
6 (from <Cite Key="wdg07"/> and <Cite Key="cdgs10"/>).
</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. Most of these are contained in published papers,
but for the convenience of the user they have been added here.

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

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