On some involution theorems on twofold Poisson manifolds
type: Item
instance of: scholarly article
title: On some involution theorems on twofold Poisson manifolds
zbMATH Open document ID: 0652.58029
DOI: 10.1007/BF00398587
published in: Letters in Mathematical Physics
publication date: 1988-01-01T00:00:00Z
review text: The author points out some involution theorems which are consequences of the existence of two compatible Poisson structures on a smooth manifold. Also using a theorem of Lichnerowicz on local triviality of the Schouten- Nijenhuis cohomology, he shows that the local exactness of a second Poisson structure with respect to the first one is equivalent with the involutivity of the algebra of smooth invariant functions of the first Poisson structure.
reviewed by: Mircea Puta
Mathematics Subject Classification ID: 37J99
zbMATH DE Number: 4064108
zbMATH Keywords: twofold Poisson manifold
zbMATH Keywords: integrability
zbMATH Keywords: involution theorems
zbMATH Keywords: Poisson structures
zbMATH Keywords: Schouten-Nijenhuis cohomology
author: Ermenegildo Caccese
MaRDI profile type: Publication
cites work: EULER EQUATIONS ON FINITE-DIMENSIONAL LIE GROUPS
cites work: Reduction techniques for infinite-dimensional Hamiltonian systems: some ideas and applications
description: scientific article; zbMATH DE number 4064108