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Mathematica™ Packages For Computing Principal Decompositions Of Simple Lie Algebras And Applications In Extended Conformal Field Theories

Author

Listed:
  • DANIELA GĂRĂJEU

    (Centre de Physique Théorique, CNRS Luminy, Case 907, 13288 Marseille Cedex 9, France)

  • MIHAIL GĂRĂJEU

    (LMMT, UPRES EA 2596, Université Aix-Marseille III, Avenue Escadrille Normandie-Niemen, Case 322, 13397 Marseille Cedex 20, France)

Abstract

In this article, we propose two Mathematica™ packages for doing calculations in the domain of classical simple Lie algebras.The main goal of the first package,$\tt{SimpleLieAlgebras.m}$, 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,$\tt{PrincipalDecomposition.m}$, 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 ofW-gravity.

Suggested Citation

  • Daniela Gărăjeu & Mihail Gărăjeu, 2003. "Mathematica™ Packages For Computing Principal Decompositions Of Simple Lie Algebras And Applications In Extended Conformal Field Theories," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-27.
    • Handle: RePEc:wsi:ijmpcx:v:14:y:2003:i:01:n:s012918310300419x
    DOI: 10.1142/S012918310300419X
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