Solutions of the classical Yang-Baxter equation and noncommutative deformations

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dc.creatorBoucetta, M.
dc.date2005-11-20
dc.date.accessioned2026-07-07T06:51:31Z
dc.date.available2026-07-07T06:51:31Z
dc.descriptionIn this paper, I will show that, if a Lie algebra $\G$ acts on a manifold $P$, any solution of the classical Yang-Baxter equation on $\G$ gives arise to a Poisson tensor on $P$ and a torsion-free and flat contravariant connection (with respect to the Poisson tensor). Moreover, if the action is locally free, the matacurvature of the above contravariant connection vanishes. This will permit to get a large class of manifolds which satisfy the necessary conditions, presented by Hawkins in math.QA/0504232, to the existence of a noncommutative deformation.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0511500
dc.identifierhttp://arxiv.org/abs/math/0511500
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/105009
dc.subjectSymplectic Geometry
dc.subjectDifferential Geometry
dc.subject53B34; Secondary 46I65, 53D17
dc.titleSolutions of the classical Yang-Baxter equation and noncommutative deformations
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