Bicrossed products induced by Poisson vector fields and their integrability
type: Item
instance of: scholarly article
title: Bicrossed products induced by Poisson vector fields and their integrability
zbMATH Open document ID: 1339.53078
DOI: 10.1142/S0219887816500225
author: Samson Apourewagne Djiba
author: Aïssa Wade
published in: International Journal of Geometric Methods in Modern Physics
publication date: 2016-04-26T00:00:00Z
Mathematics Subject Classification ID: 53D17
Mathematics Subject Classification ID: 17B62
zbMATH DE Number: 6573990
zbMATH Keywords: Poisson structures
zbMATH Keywords: Lie algebroids
zbMATH Keywords: Lie groupoids
zbMATH Keywords: cohomology
zbMATH Keywords: cosymplectic structure
zbMATH Keywords: \(L_\infty\) algebra
zbMATH Keywords: Atiyah class
Wikidata QID: Q69621921
MaRDI profile type: Publication
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review text: This paper introduces and studies the notion of cosymplectic groupoid. Let us recall that Lie algebroids are very useful to understand geometric structures on manifolds. In this work, the authors first prove the existence of a canonical Lie algebroid structure naturally associated with any Poisson vector field on a Poisson manifold, which depends only on the cohomology class of the vector field. Then, the notion of cosymplectic groupoid is developed and the integrability of the first jet bundle into a cosymplectic groupoid is investigated. Finally, the authors construct a bicrossed product and apply their construction to obtain results on \(L_\infty\) algebras and Atiyah classes.
reviewed by: Angela Gammella-Mathieu
description: scientific article; zbMATH DE number 6573990