Leibniz cohomology for differentiable manifolds

Abstract

L'accès aux archives de la revue « Annales de l'institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ * Supported by the National Science Foundation, grant no. DMS-9704891.

The Poincaré Group in a Demisemidirect Product with a Non-associative Algebra with Representations that Include Particles and Quarks—II

“…If all the (co)homology theory and the identification of the symplectic spaces remains the same in analog, then the picture for the demisemidirect product of V with p would be complete. Although specific examples have been worked out, there is as yet no general theory that will do the trick although there has been some progress [7,8]. This is a point at which we will just say that it is under consideration.…”

“…Dixon [2], and the work by J-L. Loday and T. Pirashvili [7] and J.M. Lodder [8] on Leibniz algebras and cohomology has provided the input for a resolution of this interplay between what is a (not necessarily product associative) linear vector space property and the properties of the Poincaré group.…”

Rigidity of secondary characteristic classes

“…The filtration for the Pirashvili spectral sequence [9] [11] can be immediately applied to yield a decreasing filtration {F s * } s≥0 for C * RG (g) [2]. We use the same grading as in [9] [11], which becomes F 0 * = C * RG [2], and for s ≥ 1,…”

Cohomology and Deformations of Courant Pairs

“…We will recall this cohomology in the next section for the deformation of Courant pairs. We know that the Leibniz algebra cohomology space HL * (χ( n ).) and the Lie algebra cohomology space H * (χ( n ),) are different as there are new generators for the dual Leibniz algebra structure over the Leibniz cohomology space [27,28].…”