Classification and Identification of Lie Algebras
About this ebook
for researchers and practitioners who apply Lie algebras and Lie groups
to solve problems arising in science and engineering. The authors
address the problem of expressing a Lie algebra obtained in some
arbitrary basis in a more suitable basis in which all essential
features of the Lie algebra are directly visible. This includes
algorithms accomplishing decomposition into a direct sum,
identification of the radical and the Levi decomposition, and the
computation of the nilradical and of the Casimir invariants. Examples
are given for each algorithm.
For low-dimensional Lie algebras
this makes it possible to identify the given Lie algebra completely.
The authors provide a representative list of all Lie algebras of
dimension less or equal to 6 together with their important properties,
including their Casimir invariants. The list is ordered in a way to
make identification easy, using only basis independent properties of
the Lie algebras. They also describe certain classes of nilpotent and
solvable Lie algebras of arbitrary finite dimensions for which complete
or partial classification exists and discuss in detail their
construction and properties.
The book is based on material that
was previously dispersed in journal articles, many of them written by
one or both of the authors together with their collaborators. The
reader of this book should be familiar with Lie algebra theory at an
introductory level.
Titles in this series are co-published with the Centre de Recherches Mathématiques.
