Poisson structures on cotangent bundles.
Mitric, Gabriel (2003)
International Journal of Mathematics and Mathematical Sciences
Shurygin, Vadim V.jun. (2005)
Lobachevskii Journal of Mathematics
Kenny De Commer (2015)
Banach Center Publications
On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures on these...
Jan Vysoký, Ladislav Hlavatý (2012)
Archivum Mathematicum
Poisson sigma models represent an interesting use of Poisson manifolds for the construction of a classical field theory. Their definition in the language of fibre bundles is shown and the corresponding field equations are derived using a coordinate independent variational principle. The elegant form of equations of motion for so called Poisson-Lie groups is derived. Construction of the Poisson-Lie group corresponding to a given Lie bialgebra is widely known only for coboundary Lie bialgebras. Using...
Norbert Mahoungou Moukala, Basile Guy Richard Bossoto (2016)
Archivum Mathematicum
In this paper, denotes a smooth manifold of dimension , a Weil algebra and the associated Weil bundle. When is a Poisson manifold with -form , we construct the -Poisson form , prolongation on of the -Poisson form . We give a necessary and sufficient condition for that be an -Poisson manifold.
Joseph Oesterlé (1997/1998)
Séminaire Bourbaki
Alberto S. Cattaneo, Charles Torossian (2008)
Annales scientifiques de l'École Normale Supérieure
In this article we use the expansion for biquantization described in [7] for the case of symmetric spaces. We introduce a function of two variables for any symmetric pairs. This function has an expansion in terms of Kontsevich’s diagrams. We recover most of the known results though in a more systematic way by using some elementary properties of this function. We prove that Cattaneo and Felder’s star product coincides with Rouvière’s for any symmetric pairs. We generalize some of Lichnerowicz’s...
Dimitri Gurevich, Pavel Saponov (2011)
Banach Center Publications
We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and...
Chiara Esposito (2015)
Banach Center Publications
In this paper we recall the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group theories.
F. Bonechi, M. Tarlini, N. Ciccoli (2003)
Banach Center Publications
We describe how the constructions of quantum homogeneous spaces using infinitesimal invariance and quantum coisotropic subgroups are related. As an example we recover the quantum 4-sphere of [2] through infinitesimal invariance with respect to .
Kentaro Mikami, Alan Weinstein (2000)
Banach Center Publications
We study the group of diffeomorphisms of a 3-dimensional Poisson torus which preserve the Poisson structure up to a constant multiplier, and the group of similarity ratios.
Giunashvili, Z. (1998)
Georgian Mathematical Journal
Calaque, Damien, Rossi, Carlo A. (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Simon Hochgerner, Armin Rainer (2006)
Revista Matemática Complutense
We consider the Poisson reduced space (T* Q)/K, where the action of the compact Lie group K on the configuration manifold Q is of single orbit type and is cotangent lifted to T* Q. Realizing (T* Q)/K as a Weinstein space we determine the induced Poisson structure and its symplectic leaves. We thus extend the Weinstein construction for principal fiber bundles to the case of surjective Riemannian submersions Q → Q/K which are of single orbit type.
Jean-Paul Dufour (2000)
Banach Center Publications
Jacek Dębecki (2006)
Czechoslovak Mathematical Journal
We establish a formula for the Schouten-Nijenhuis bracket of linear liftings of skew-symmetric tensor fields to any Weil bundle. As a result we obtain a construction of some liftings of Poisson structures to Weil bundles.
Jean-Paul Dufour, Aïssa Wade (2006)
Annales de l’institut Fourier
We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first-order approximation (not necessarily linear) of a given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular...
Stéphane Druel (1999)
Bulletin de la Société Mathématique de France
P. M. Kouotchop Wamba, A. Ntyam (2013)
Archivum Mathematicum
The tangent lifts of higher order of Dirac structures and some properties have been defined in [9] and studied in [11]. By the same way, the tangent lifts of higher order of Poisson structures have been studied in [10] and some applications are given. In particular, the authors have studied the nature of the Lie algebroids and singular foliations induced by these lifting. In this paper, we study the tangent lifts of higher order of multiplicative Poisson structures, multiplicative Dirac structures...
Izu Vaisman (2000)
Annales Polonici Mathematici
We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give new examples of Lie bialgebroids over Poisson manifolds.