Graded Poisson structures on the algebra of differential forms
type: Item
instance of: scholarly article
title: Graded Poisson structures on the algebra of differential forms
zbMATH Open document ID: 0844.58025
DOI: 10.1007/BF02566014
published in: Commentarii Mathematici Helvetici
publication date: 1996-02-22T00:00:00Z
full work available at URL: https://eudml.org/doc/140375
review text: The Koszul-Schouten bracket, i.e. a Poisson bracket extended to all differential forms \(\Omega (M)\), is described by means of graded derivations on \(\Omega (M)\). The analogous problem for graded symplectic forms is studied. In the non-degenerate case, the Koszyl-Schouten bracket comes from a graded symplectic exact form. On the other hand it is shown that any odd symplectic form is the image of a graded symplectic form on \(\Omega (M)\) of \(\mathbb{Z}\)-degree 1 by the pullback of an automorphism of the algebra \(\Omega (M)\). For applications see also [\textit{J. Monterde}, Differ. Geom. Appl. 2, No. 1, 81-97 (1992; Zbl 0789.53020)], [\textit{A. P. Nersessian}, JETP Lett. 58, No. 1, 66-70 (1993); translation from Puma Zh. Eksper. Teoret. Fiz. 58, No. 1, 64-68 (1993)]\ and [\textit{A. Schwarz}, Commun. Math. Phys. 155, No. 2, 249-260 (1993; Zbl 0786.58017)].
reviewed by: Maido Rahula
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 58A50
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 838577
zbMATH Keywords: graded symplectic forms
zbMATH Keywords: Koszul-Schouten bracket
author: José V. Beltrán
author: Juan Monterde
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 838577