Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions

Beitrag in einem Sammelwerk

Details zur Publikation

Autor(en): Neeb KH, Thiemann T, Sahlmann H
Herausgeber: V. Dobrev
Titel Sammelwerk: Springer Proceedings in Mathematics & Statistics
Verlag: Springer Japan
Jahr der Veröffentlichung: 2015
Band: 111
Seitenbereich: 105-136
ISBN: 978-4-431-55284-0


We introduce a notion of a weak Poisson structure on a manifold M modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra A⊆C∞(M)" id="MathJax-Element-1-Frame" role="presentation" style="position: relative;" tabindex="0">A⊆C∞(M) which has to satisfy a non-degeneracy condition (the differentials of elements of A" id="MathJax-Element-2-Frame" role="presentation" style="position: relative;" tabindex="0">A separate tangent vectors) and we postulate the existence of smooth Hamiltonian vector fields. Motivated by applications to Hamiltonian actions, we focus on affine Poisson spaces which include in particular the linear and affine Poisson structures on duals of locally convex Lie algebras. As an interesting byproduct of our approach, we can associate to an invariant symmetric bilinear form κ on a Lie algebra g" id="MathJax-Element-3-Frame" role="presentation" style="position: relative;" tabindex="0">g and a κ-skew-symmetric derivation D a weak affine Poisson structure on g" id="MathJax-Element-4-Frame" role="presentation" style="position: relative;" tabindex="0">g itself. This leads naturally to a concept of a Hamiltonian G-action on a weak Poisson manifold with a g" id="MathJax-Element-5-Frame" role="presentation" style="position: relative;" tabindex="0">g

-valued momentum map and hence to a generalization of quasi-hamiltonian group actions.


FAU-Autoren / FAU-Herausgeber

Neeb, Karl-Hermann Prof. Dr.
Lehrstuhl für Mathematik
Sahlmann, Hanno Prof. Dr.
Professur für Theoretische Physik
Thiemann, Thomas Prof. Dr.
Lehrstuhl für Theoretische Physik


Neeb, K.-H., Thiemann, T., & Sahlmann, H. (2015). Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions. In V. Dobrev (Eds.), Springer Proceedings in Mathematics & Statistics. (pp. 105-136). Springer Japan.

Neeb, Karl-Hermann, Thomas Thiemann, and Hanno Sahlmann. "Weak Poisson structures on infinite dimensional manifolds and hamiltonian actions." Springer Proceedings in Mathematics & Statistics. Ed. V. Dobrev, Springer Japan, 2015. 105-136.


Zuletzt aktualisiert 2019-13-05 um 13:15