Displaying similar documents to “Estimates for the Poisson kernel on higher rank NA groups”

Computation of Biharmonic Poisson Kernel for the Upper Half Plane

Ali Abkar (2007)

Bollettino dell'Unione Matematica Italiana

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We first consider the biharmonic Poisson kernel for the unit disk, and study the boundary behavior of potentials associated to this kernel function. We shall then use some properties of the biharmonic Poisson kernel for the unit disk to compute the analogous biharmonic Poisson kernel for the upper half plane.

Quantization of pencils with a gl-type Poisson center and braided geometry

Dimitri Gurevich, Pavel Saponov (2011)

Banach Center Publications

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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...

Nambu-Poisson Tensors on Lie Groups

Nobutada Nakanishi (2000)

Banach Center Publications

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First as an application of the local structure theorem for Nambu-Poisson tensors, we characterize them in terms of differential forms. Secondly left invariant Nambu-Poisson tensors on Lie groups are considered.

Linearization and star products

Veronique Chloup (2000)

Banach Center Publications

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The aim of this paper is to give an overview concerning the problem of linearization of Poisson structures, more precisely we give results concerning Poisson-Lie groups and we apply those cohomological techniques to star products.

Poisson–Lie sigma models on Drinfel’d double

Jan Vysoký, Ladislav Hlavatý (2012)

Archivum Mathematicum

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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....

A note on n-ary Poisson brackets

Michor, Peter W., Vaisman, Izu

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An n -ary Poisson bracket (or generalized Poisson bracket) on the manifold M is a skew-symmetric n -linear bracket { , ⋯ , } of functions which is a derivation in each argument and satisfies the generalized Jacobi identity of order n , i.e., ∑ σ ∈ S 2 n - 1 ( sign σ ) { { f σ 1 , ⋯ , f σ n } , f σ n + 1 , ⋯ , f σ 2 n - 1 } = 0 , S 2 n - 1 being the symmetric group. The notion of generalized Poisson bracket was introduced by et al. in [J. Phys. A, Math. Gen. 29, No. 7, L151–L157 (1996; Zbl 0912.53019) and J. Phys. A, Math. Gen. 30, No. 18, L607–L616 (1997; Zbl 0932.37056)]....