IJPAM: Volume 60, No. 4 (2010)

COMPUTING COORDINATES ON LIE GROUPS

Philip Feinsilver$^1$, Uwe Franz$^2$, René Schott$^3$
$^1$Department of Mathematics
Southern Illinois University
Carbondale, IL 62901, USA
$^2$Département de Mathématiques
Université de Franche-Comté
Besançon, 25000, FRANCE
$^3$Institut Élie Cartan - Nancy and
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