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Mathematica (Tm) Packages for Computing Principal Decompositions of Simple Lie Algebras and Applications in Extended Conformal Field Theories

Daniela Garajeu
Organization: CNRS Luminy, Case 907
Department: Centre de Physique Theorique
Mihail Garajeu
Organization: Universite Aix-Marseille III
Department: LMMT, UPRES EA 2596
Journal / Anthology

International Journal of Modern Physics C
Year: 2003
Volume: 14
Page range: 1-27

In this article, we propose two MathematicaTM packages for doing calculations in the domain of classical simple Lie algebras.

The main goal of the first package, SimpleLieAlgebras.m, is to determine the principal three-dimensional subalgebra of a simple Lie algebra. The package provides several functions which give some elements related to simple Lie algebras (generators in fundamental and adjoint representation, roots, Killing form, Cartan matrix, etc.).

The second package, PrincipalDecomposition.m, concerns the principal decomposition of a Lie algebra with respect to the principal three-dimensional embedding.

These packages have important applications in extended two-dimensional conformal field theories. As an example, we present an application in the context of the theory of W-gravity.

*Mathematics > Algebra > Group Theory

Simple Lie algebra, principal decomposition, primary fields, W-algebra, conformal field theory