Poisson bivectors on infinite dimensional manifolds

Peter W. Michor and Praful Rahangdale

Address:
Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria.
Institut für Mathematik, Universität Paderborn, Warburger Str. 100, 33098 Paderborn,Germany

E-mail:
Peter.Michor@univie.ac.at
praful@math.uni-paderborn.de

Abstract: We show that, on a smoothly paracompact convenient manifold $M$ modeled on a convenient space with the bornological approximation property, the dual map of a Poisson bracket factors as a smooth section of the vector bundle $L_{\text{skew}}^2(T^*M,\mathbb{R})$.

AMSclassification: primary 58B20; secondary 70G70, 70G45.

Keywords: Poisson structure, Poisson bivector, infinite dimensional manifolds.

DOI: 10.5817/AM2026-3-113