Related papers: Newton polyhedra and Poisson structures from certa…
Symmetries of Poisson manifolds are in general quantized just to symmetries up to homotopy of the quantized algebra of functions. It is therefore interesting to study symmetries up to homotopy of Poisson manifolds. We notice that they are…
A Poisson system is a Poisson point process and a group action, together forming a measure-preserving dynamical system. Ornstein and Weiss proved Poisson systems over many amenable groups were isomorphic in their 1987 paper. We consider…
We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and…
In this text we give a decomposition result on polynomial poly-vector fields generalizing a result on the decomposition of homogeneous Poisson structures. We discuss consequences of this decomposition result in particular for low dimensions…
Several types of generically-nondegenerate Poisson structures can be effectively studied as symplectic structures on naturally associated Lie algebroids. Relevant examples of this phenomenon include log-, elliptic, $b^k$-, scattering and…
Motivated by the recent connection between nonholonomic integrable systems and twisted Poisson manifolds made in \cite{balseiro_garcia_naranjo}, this paper investigates the global theory of integrable Hamiltonian systems on almost…
We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri-Morosi and…
We demonstrate the construction of Poisson structures via Lie algebroids on moduli spaces of twisted stable Higgs bundles over stacky curves. The construction provides new examples of Poisson structures on such moduli spaces. Special…
We consider the problem of integrability of the Poisson equations describing spatial motion of a rigid body in the classical nonholonomic Suslov problem. We obtain necessary conditions for their solutions to be meromorphic and show that…
A new invariant of Poisson manifolds, a Poisson K-ring, is introduced. Hypothetically, this invariant is more tractable than such invariants as Poisson (co)homology. A version of this invariant is also defined for arbitrary algebroids.…
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…
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is that quadratic…
This paper is devoted to a systematic study of the geometry of nondegenerate $\bbR^n$-actions on $n$-manifolds. The motivations for this study come from both dynamics, where these actions form a special class of integrable dynamical systems…
Any classical r-matrix on the Lie algebra of linear operators on a real vector space V gives rise to a quadratic Poisson structure on V which admits a deformation quantization stemming from the construction of V. Drinfel'd. We exhibit in…
In this paper we extensively study the notion of Hamiltonian structure for nonabelian differential-difference systems, exploring the link between the different algebraic (in terms of double Poisson algebras and vertex algebras) and…
We construct a hierarchy of integrable systems whose Poisson structure corresponds to the BMS$_{3}$ algebra, and then discuss its description in terms of the Riemannian geometry of locally flat spacetimes in three dimensions. The analysis…
We establish the plurisubharmonicity of the envelope of the Poisson functional on almost complex manifolds. That is, we generalize the corresponding result for complex manifolds and almost complex manifolds of complex dimension two.
The graph complex acts on the spaces of Poisson bi-vectors $P$ by infinitesimal symmetries. We prove that whenever a Poisson structure is homogeneous, i.e. $P = L_{\vec{V}}(P)$ w.r.t. the Lie derivative along some vector field $\vec{V}$,…
In this paper we develop a geometric version of the Hamilton-Jacobi equation in the Poisson setting. Specifically, we "geometrize" what is usually called a complete solution of the Hamilton-Jacobi equation. We use some well-known results…
In recent years, $b$-symplectic manifolds have become important structures in the study of symplectic geometry, serving as Poisson manifolds that retain symplectic properties away from a hypersurface. Inspired by this rich landscape,…