Classifying solvable Lie algebras with Magma
Willem de Graaf
Trento
This talk is divided into two parts. The first part is about finding
the classification of small-dimensional solvable Lie algebras. This is
done by extending a solvable Lie algebra of smaller dimansion by a
derivation. Subsequently, the Groebner basis facilities of Magma are
used to find isomorphisms, and obtain a non-redundant list. This procedure
has been used to find the classification of the solvable Lie algebras
of dimensions 3, 4.
The second part is about the electronic version of the classification
of the solvable Lie algebras. I have written Magma functions for
constructing the Lie algebras that appear in the classification. This
is complemented by a function that, given a solvable Lie algebra of
dimension <= 4, finds an isomorphism with a Lie algebra from the
classification. Here Groebner bases are no longer used; the algorithm
is based on the proof of the correctness of the classification.