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Yang-Mills equations and solvable groups. II

par Cahen, Michel ;Gutt, Simone ;Kozameh, Carlos;Newman, Ezra
Référence Journal of mathematical physics, 29, 4, page (1022-1025)
Publication Publié, 1988

Article révisé par les pairs

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Résumé :

It is shown that the necessary and sufficient condition for the Yang-Mills equations (associated with an arbitrary group G) to be derivable from a Lagrangian (which is polynomial in the derivatives of the connection) is that the Lie algebra sript g sign of G possesses an invariant nondegenerate quadratic form γ. It is well known that for semisimple groups such a γ exists, namely the Killing form. What is not so well known is that such a γ exists for many other groups and in particular for many solvable and nilpotent groups. Several examples in this class are discussed. © 1988 American Institute of Physics.