Related papers: Bott Connection and Generalized Functions on Poiss…

A novel gravity theory based on Poisson Generalized Geometry is investigated. A gravity theory on a Poisson manifold equipped with a Riemannian metric is constructed from a contravariant version of the Levi-Civita connection, which is based…

The formulation of covariant brackets on the space of solutions to a variational problem is analyzed in the framework of contact geometry. It is argued that the Poisson algebra on the space of functionals on fields should be read as a…

Inspired by the geometric bracket for the generalized covariant Hamilton system, we abstractly define a generalized geometric commutator $$\left[ a,b \right]={{\left[ a,b \right]}_{cr}}+G\left(s,a,b \right)$$ formally equipped with…

This is the first in a series of papers dedicated to the study of Poisson manifolds of compact types (PMCTs). This notion encompasses several classes of Poisson manifolds defined via properties of their symplectic integrations. In this…

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the algebra of functions on X is in one-to-one…

We study the general form of the *-commutator treated as a deformation of the Poisson bracket on the Grassman algebra. We show that, up to a similarity transformation, there are other deformations of the Poisson bracket in addition to the…

We construct a first order local model for Poisson manifolds around a large class of Poisson submanifolds and we give conditions under which this model is a local normal form. The resulting linearization theorem includes as special cases…

We study the Poisson bracket invariant, which measures the level of Poisson noncommutativity of a smooth partition of unity, on closed symplectic surfaces. Motivated by a general conjecture of Polterovich and building on preliminary work of…

The concept of generalized functions taking values in a differentiable manifold is extended to a functorial theory. We establish several characterization results which allow a global intrinsic formulation both of the theory of…

We introduce a noncommutative Poisson random measure on a von Neumann algebra. This is a noncommutative generalization of the classical Poisson random measure. We call this construction Poissonization. Poissonization is a functor from the…

A few generalizations of a Poisson algebra to field theory canonically formulated in terms of the polymomentum variables are discussed. A graded Poisson bracket on differential forms and an $(n+1)$-ary bracket on functions are considered.…

We define and characterize spaces of manifold-valued generalized functions and generalized vector bundle homomorphisms in the setting of the full diffeomorphism-invariant vector-valued Colombeau algebra. Furthermore, we establish point…

We discuss the relationship between the multiple Hamiltonian structures of the generalized Toda lattices and that of the generalized Volterra lattices. We use a symmtery approach for Poisson structures that generalizes the Poisson…

Using the notion of a contravariant derivative, we give some algebraic and geometric characterizations of Poisson algebras associated to the infinitesimal data of Poisson submanifolds. We show that such a class of Poisson algebras provides…

We consider the space of graph connections (lattice gauge fields) which can be endowed with a Poisson structure in terms of a ciliated fat graph. (A ciliated fat graph is a graph with a fixed linear order of ends of edges at each vertex.)…

Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\"ahler differentials of A depending naturally on A and the Poisson bracket. This…

We review the prequantization procedure in the context of super symplectic manifolds with a symplectic form which is not necessarily homogeneous. In developing the theory of non homogeneous symplectic forms, there is one surprising result:…

In this paper, we consider Hamiltonian structures of hydrodynamic type and some of their generalizations. In particular, we discuss the questions concerning the structure and special forms of the corresponding Poisson brackets and the…

The Poisson bracket algebra corresponding to the second Hamiltonian structure of a large class of generalized KdV and mKdV integrable hierarchies is carefully analysed. These algebras are known to have conformal properties, and their…

On a polarized compact symplectic manifold endowed with an action of a compact Lie group, in analogy with geometric invariant theory, one can define the space of invariant functions of degree k. A central statement in symplectic geometry,…