Note on moufang-noether currents

Abstract

The derivative Noether currents generated by continuous Moufang tranformations are constructed and their equal-time commutators are found. The corresponding charge algebra turns out to be a birepresentation of the tangent Mal'ltsev algebra of an analytic Moufang loop.

Moufang loops and generalized Lie-Cartan theorem

“…By taking g = e, the commutation relations (1) − (6) give the Lie algebra of the multiplication group of the birepresentation (S, T ) of G. For field theoretical applications see [6].…”

“…In particular, it was recently shown [6] how the Moufang-Noether current algebras may be constructed so that the corresponding Noether charge algebra turns out to be a birepresentation of the tangent Mal'tsev algebra of an analytic Moufang loop.…”

Moufang loops and generalized Lie-Cartan theorem1

“…The Jacobi identities are guaranteed by the defining identities of the Lie [7] and general Lie triple systems [8,9] associated with the derivative Mal'tsev algebra of T e (G) of G. The commutation relations of form (1) − (6) are well known from the theory of alternative algebras [10]. By taking g = e, the commutation relations (1) − (6) give the Lie algebra of the multiplication group of the birepresentation (S, T ) of G. For field theoretical applications see [6].…”