IJPAM: Volume 60, No. 4 (2010)




Southern Illinois University
Carbondale, IL 62901, USA

Université de Franche-Comté
Besançon, 25000, FRANCE

Laboratoire Lorrain de Recherche en Informatique et ses Applications
(IECN and LORIA)
Université Henri Poincaré
Nancy 1, P.O. Box 239, Vandoeuvre-lès-Nancy Cedex, 54506, FRANCE
Abstract.We present a method for computing coordinates of the second kind on Lie groups and explain
connections with representations. The approach is especially
effective for Lie algebras admitting flags of subalgebras, including
solvable (hence nilpotent) Lie algebras. A simple
diagrammatic technique is developed that expresses the results directly in terms of the
structure constants of the Lie algebra. We show how to do the
calculations by symbolic computation with MAPLE.
Received: August 20, 2008
AMS Subject Classification: 17Bxx
Key Words and Phrases: Lie algebras, coordinates of the second kind, flags, symbolic computation
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 60
Issue: 4