What's this?
This page contains some
GAP 4
files
that can be used to access the experimental classification of nilpotent
Lie algebras of
dimension at most 9 over GF(2) and those of dimension at most 7 over
GF(3)
and GF(5).
How?
Download the two files below. The file
smallliealgdata.gi
contains the algebras
in a special compressed format, while the file
smalllie.gi
contains some
programs that can interpret the data in
smallliealgdata.gi.
Edit the beginning of the
smalllie.gi file and set the
SMALL_LIE_DATA_FILE
variable to contain the full path of the
smallliealgdata.gi
file.
Read the
smallliealg.gi file in your GAP 4 process:
gap> Read( "smallliealg.gi" );
Then the function call
SmallLieAlgebra( F, dim, n ) returns the
n-th nilpotent
Lie algebra with dimension
dim over the field
F.
Here is an example:
gap> L := SmallLieAlgebra( GF(3), 7, 120 );
<Lie algebra of dimension 7 over GF(3)>
gap> LieLowerCentralSeries( L );
[ <
Lie algebra of dimension 7 over GF(3)>,
< Lie algebra of dimension 4 over GF( 3 )>,
<Lie algebra of dimension 2 over GF(3)>,
<Lie algebra of dimension 1 over GF(3)>,
<Lie algebra of dimension 0 over GF(3)> ]
As said before, you can access the nilpotent Lie algebras of dimension
at most 9 over GF(2) and those of dimension at most 7 over GF(3) and
GF(5). Expect an error message if you try any other parameter.
Download
smalllie.gi: [
uncompressed] [
gzipped]
smallliealgdata.gi: [
uncompressed]
[
gzipped]
Csaba Schneider
17 June 2004