Computation of invariants of Lie algebras by means of moving frames

Abstract:
A new purely algebraic algorithm is presented for computation of invariants (generalized Casimir operators) of general Lie algebras over the real or complex number field. It uses the Cartan's method of moving frames and the knowledge of the group of inner automorphisms of each Lie algebra. Invariants of wide classes of Lie algebras are calculated to illustrate its effectiveness and to make a comparison with the same cases in the literature. The investigated algebras cover the low-dimensional Lie algebras and families of solvable Lie algebras of general dimension, which are distinguished by the structure of the nilradicals of their Lie algebras.

Joint work with Jiri Patera (Centre de Recherches Mathématiques, Université de Montréal, Canada) and Roman Popovych (Institute of Mathematics of NAS of Ukraine, Kyiv, Ukraine & University of Vienna, Austria).