• ### q-Multivector fields and q-forms on Weil bundles

Olivier MABIALA MIKANOU, Borhen Vann NKOU, Basile Guy Richard BOSSOTO

Université Marien NGOUABI , BP: 69, Brazzaville, Congo.

Abstract: Let M be a paracompact smooth manifold of dimension n, A a Weil algebra and M^A the associated Weil bundle. In this paper, we define the Schouten-Nijenhuis bracket on the C∞(M^A, A)-module X*(M^A) of multivector fields on M^A considered as multi-derivations from C∞(M) into C∞(M^A, A) and we show that the exterior algebra X*(M^A) of multivector fields on M^A is a Lie graded algebra over A. To finish, we estabish an isomorphism between X^q(M^A) and the C∞(M^A, A)-module Lalt^q(Ω(M^A, A), C∞(M^A, A)) of skew-symmetric multilinear forms of degree q onto the C∞(M^A, A)-module Ω(M^A, A) of differential A-forms on M^A.

Keywords: Weil bundle, Weil algebra, Multivector fields, Schouten-Nijenhuis bracket.