Related papers: Noncommutative Poisson structures on Orbifolds

An anologue of the Calabi invariant for Poisson manifolds is considered. For any Poisson manifold $P$, the Poisson bracket on $C^{\infty}(P)$ extends to a Lie bracket on the space $\Omega^{1}(P)$ of all differential one-forms, under which…

A class of nongraded Hamiltonian Lie algebras was earlier introduced by Xu. These Lie algebras have a Poisson bracket structure. In this paper, the isomorphism classes of these Lie algebras are determined by employing a ``sandwich'' method…

We give a method to construct Poisson brackets $\{\cdot,\cdot\}$ on Banach manifolds~$M$, for which the value of $\{f,g\}$ at some point $m\in M$ may depend on higher order derivatives of the smooth functions $f,g\colon M\to{\mathbb R}$,…

We obtain a complete group classification of the Lie point symmetries of nonlinear Poisson equations on generic (pseudo) Riemannian manifolds M. Using this result we study their Noether symmetries and establish the respective conservation…

We study higher-degree generalizations of symplectic groupoids, referred to as {\em multisymplectic groupoids}. Recalling that Poisson structures may be viewed as infinitesimal counterparts of symplectic groupoids, we describe "higher''…

We introduce the notion of a $\theta$-almost twisted Poisson structure on manifolds, which involves incorporating a closed $1$-form $\theta$ into twisted Poisson structures under specific conditions. We provide a characterization of this…

The Higgs sector of the low-energy physics of n of coincident D-branes contains the necessary elements for constructing noncommutative manifolds. The coordinates orthogonal to the coincident branes, as well as their conjugate momenta, take…

Global constructions of quantization deformation and obstructions are discussed for an arbitrary complex analytic space in terms of adapted (analytic) Hochschild cohomology. For K3-surfaces an explicit global construction of a Poisson…

We generalize to the homotopy case a result of K. Mackenzie and P. Xu on relation between Lie bialgebroids and Poisson geometry. For a homotopy Poisson structure on a supermanifold $M$, we show that $(TM, T^*M)$ has a canonical structure of…

We construct the family of algebroid brackets $[\cdot,\cdot]_{c,v}$ on the tangent bundle $T^*M$ to a Poisson manifold $(M,\pi)$ starting from an algebroid bracket of differential forms. We use these brackets to generate Poisson structures…

Let X be a an affine smooth symplectic variety over $\mathbb{Z}/p\mathbb{Z},$ and A be its deformation quantization over the p-adic integers. We prove that for all $n\geq 1,$ the Hochschild cohomogy of $A/p^nA$ is isomorphic to the de…

Let X be a compact Kahler manifold with a non-trivial holomorphic Poisson structure. Then there exist deformations of non-trivial generalized Kahler structures with one pure spinor on X. We prove that every Poisson submanifold of X is a…

We show that Hochschild cohomology of an algebra over a field is a space of infinity coderivations on an arbitrary projective bimodule resolution of the algebra. The Gerstenhaber bracket is the graded commutator of infinity coderivations.…

Let X be a complex manifold with strongly pseudoconvex boundary M. If u is a defining function for M, then -log u is plurisubharmonic on a neighborhood of M in X, and the (real) 2-form s = i \del \delbar(-log u) is a symplectic structure on…

Let $K$ be a compact group. For a symplectic quotient $M_{\lambda}$ of a compact Hamiltonian K\"ahler $K$-manifold, we show that the induced complex structure on $M_{\lambda}$ is locally invariant when the parameter $\lambda$ varies in…

In this paper, we generalize the geometry of the product pseudo-Riemannian manifold equipped with the product Poisson structure (\cite{Nas2}) to the geometry of a warped product of pseudo-Riemannian manifolds equipped with a warped Poisson…

In this paper, we consider the hamiltonian formulation of nonholonomic systems with symmetries and study several aspects of the geometry of their reduced almost Poisson brackets, including the integrability of their characteristic…

We present a geometric construction of irreversible dynamics on Poisson manifolds that satisfies the axioms of metriplectic mechanics and the GENERIC framework. Our approach relies solely on the underlying Poisson structure and its…

Poisson algebra is usually defined to be a commutative algebra together with a Lie bracket, and these operations are required to satisfy the Leibniz rule. We describe Poisson structures in terms of a single bilinear operation. This enables…

We classify pairs $(M,G)$ where $M$ is a $3$--dimensional simply connected smooth manifold and $G$ a Lie group acting on $M$ transitively, effectively with compact isotropy group.