Poisson cohomology in dimension three.
type: Item
instance of: scholarly article
title: Poisson cohomology in dimension three.
zbMATH Open document ID: 1070.53051
author: Anne Pichereau
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2005-02-23T00:00:00Z
review text: The author considers the affine space F3 and describes the Poisson cohomology for Poisson structures on F3 in the case when there is a quasi-homogeneous Casimir. The Poisson cohomology, introduced by Lichnerowicz, plays an important role in the study of Poisson deformations. However, its computation in the general case is very difficult. In this paper, the author describes this cohomology for the affine space F3 which admits a quasi-homogeneous Casimir \(\phi\) and a singular locus reduced to the origin. She proves that this cohomology is strongly related to the singularity of the surface defined by the zero of \(\phi\).
reviewed by: Angela Gammella-Mathieu
Mathematics Subject Classification ID: 53D17
zbMATH DE Number: 2138004
zbMATH Keywords: Poisson cohomology
zbMATH Keywords: Poisson structures
zbMATH Keywords: Casimir
MaRDI profile type: Publication
full work available at URL: j.crma.2004.11.020
OpenAlex ID: W2039845403
cites work: Les variétés de Poisson et leurs algèbres de Lie associees
cites work: Poisson cohomology in dimension two
cites work: Poisson cohomology of the affine plane
cites work: Gerstenhaber algebras and BV-algebras in Poisson geometry
DOI: 10.1016/J.CRMA.2004.11.020
description: scientific article; zbMATH DE number 2138004