Algebraic Nijenhuis operators and Kronecker Poisson pencils
نویسندگان
چکیده
منابع مشابه
Algebraic Nijenhuis operators and Kronecker Poisson pencils
This paper is devoted to a method of constructing completely integrable systems based on the micro-local theory of bihamiltonian structures [GZ89, GZ91, Bol91, GZ93, GZ00, Pan00, Zak01]. The main tool are the so-called microKronecker bihamiltonian structures [Zak01], which will be called Kronecker in this paper for short (in [GZ00] the term Kronecker was used for the micro-Kronecker structures ...
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We construct Nijenhuis operators from particular bialgebras called dendriform-Nijenhuis bialgebras. It turns out that such Nijenhuis operators commute with TD-operators, a kind of Baxter-Rota operators, and are therefore closely related to dendriform trialgebras. This allows the construction of associative algebras, called dendriform-Nijenhuis algebras, made out of nine operations and presentin...
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Article history: Received 28 December 2012 Available online 14 June 2013 Communicated by T.S. Ratiu MSC: 37K10 53D17 53A60 A Poisson pencil is called flat if all brackets of the pencil can be simultaneously locally brought to a constant form. Given a Poisson pencil on a 3-manifold, we study under which conditions it is flat. Since the works of Gelfand and Zakharevich, it is known that a pencil ...
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In this note we study generalizations in many directions of the contraction procedure for Lie algebras introduced by Saletan [Sa]. We consider products of arbitrary nature, not necessarily Lie brackets, and we generalize to infinite dimension, considering a modification of the approach by Nijenhuis tensors to bilinear operations on sections of finite-dimensional vector bundles. We apply our gen...
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ژورنال
عنوان ژورنال: Differential Geometry and its Applications
سال: 2006
ISSN: 0926-2245
DOI: 10.1016/j.difgeo.2006.05.009