Title: Automatic classification of automorphisms of lower-dimensional Lie algebras,
Abstract: We implement two algorithms in MATHEMATICA for classifying automorphisms of
lower-dimensional non-commutative Lie algebras. The first algorithm is a
brute-force approach whereas the second is an evolutionary strategy. These
algorithms are delivered as the MATHEMATICA package cwsAutoClass. In order to
facilitate the application of this package to symmetry Lie algebras of
differential equations, we also provide a package, cwsLieSymTools, for
manipulating finite-dimensional Lie algebras of vector fields. In particular,
this package allows the computations of Lie brackets, structure constants, and
the visualization of commutator tables. Several examples are provided to
illustrate the pertinence of our approach.