Related papers: Poisson bundles over unordered configurations

Using the Atiyah class we give a criterion for a vector bundle on a coisotropic subvariety, $Y$, of an algebraic Poisson variety $X$ to admit a first and second order noncommutative deformation. We also show noncommutative deformations of a…

We prove various results in infinite-dimensional differential calculus which relate differentiability properties of functions and associated operator-valued functions (e.g., differentials). The results are applied in two areas: 1. in the…

In this paper we construct indecomposable vector bundles associated to monads on Cartesian products of odd dimension projective spaces. Specifically we establish the existence of monads on…

The standard formulation of Jacobi manifolds in terms of differential operators on line bundles, although effective at capturing most of the relevant geometric features, lacks a clear algebraic interpretation similar to how Poisson algebras…

This paper presents a generalization of symplectic geometry to a principal bundle over the configuration space of a classical field. This bundle, the vertically adapted linear frame bundle, is obtained by breaking the symmetry of the full…

Generalized contact bundles are odd dimensional analogues of generalized complex manifolds. They have been introduced recently and very little is known about them. In this paper we study their local structure. Specifically, we prove a local…

First, we review the notion of a Poisson structure on a noncommutative algebra due to Block-Getzler and Xu and introduce a notion of a Hamiltonian vector field on a noncommutative Poisson algebra. Then we describe a Poisson structure on a…

We show that, on a smoothly paracompact convenient manifold $M$ modeled on a convenient space with the bornological approximation property, the dual map of a Poisson bracket factors as a smooth section of the vector bundle…

We construct a non-commutative analogue of the modular vector field on a Poisson manifold for a given pair of a double bracket and a connection on a space of 1-forms. The key ingredient, the triple divergence map, is directly constructed…

Peierls brackets are part of the space-time approach to quantum field theory, and provide a Poisson bracket which, being defined for pairs of observables which are group invariant, is group invariant by construction. It is therefore well…

We semiclassicalise the theory of quantum group principal bundles to the level of Poisson geometry. The total space $X$ is a Poisson manifold with Poisson-compatible contravariant connection, the fibre is a Poisson-Lie group in the sense of…

A vertical exterior derivative is constructed that is needed for a graded Poisson structure on multisymplectic manifolds over nontrivial vector bundles. In addition, the properties of the Poisson bracket are proved and first examples are…

We prove that the $\mathbb{R}-$algebra $\mathcal{S}(\mathcal{P}(E,M)) $ of symbols of differential operators acting on the sections of the vector bundle $E\to M$ decompose into the sum \[ \mathcal{S}(\mathcal{P}(E,M))=\mathcal{J}(E)\oplus…

We construct a mixed Hodge structure on the topological K-theory of smooth Poisson varieties, depending weakly on a choice of compactification. We establish a package of tools for calculations with these structures, such as functoriality…

We suggest a geometric approach to quantisation of the twisted Poisson structure underlying the dynamics of charged particles in fields of generic smooth distributions of magnetic charge, and dually of closed strings in locally…

We construct quadratic finite-dimensional Poisson algebras and their quantum versions related to rank N and degree one vector bundles over elliptic curves with n marked points. The algebras are parameterized by the moduli of curves. For N=2…

Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left…

Let M be a paracompact smooth manifold, A a Weil algebra and M^{A} the associated Weil bundle. In this paper, we give a characterization of hamiltonian field on M^{A} in the case of Poisson manifold and of Symplectic manifold.

The algebra S of symmetric invariants over the field with two elements is an unstable algebra over the Steenrod algebra A, and is isomorphic to the mod two cohomology of BO, the classifying space for vector bundles. We provide a minimal…

By means of techniques from the Morita equivalence theory, we get finitely generated and projective modules over the quantum Heisenberg manifolds. This enables us to get some information about the range of the trace of these algebras, at…