On the identification of a Lie algebra given by its structure constants. I: Direct decompositions, Levi decompositions, and nilradicals
In this nice article the authors give the theoretical foundation for an algorithmic identification of finite-dimensional Lie algebras starting with their commutator relations and structure constants. This algorithm is the basis for corresponding computer programs presented in the paper reviewed above and answers the following questions for a Lie algebra L: - Is L decomposable as the direct sum of Lie algebras ? - If not so, is L simple or solvable ? - If not so, how to find the radical and the Levi decomposition of L ? - If L is solvable, how to find the nilradical? The answers are given by a transformation to a canonical basis, where basis elements are grouped together corresponding to decompositions, ideals etc. The explanation at first is rather elementary and then based on representation theory, linear algebra and Lie algebra methods. For the determination of nilradicals a new algorithm working without any irrational calculations is used. Pregnant examples are given, the algorithm seems to be very useful with respect to the determination of symmetry Lie algebras of differential equations.
scientific article; zbMATH DE number 4093693
scientific article