Related papers: Essential variational Poisson cohomology

We construct differential equivariant K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct…

Let $\mathfrak g$ be a semisimple Lie algebra, $\vartheta\in {\sf Aut}(\mathfrak g)$ a finite order automorphism, and $\mathfrak g_0$ the subalgebra of fixed points of $\vartheta$. Recently, we noticed that using $\vartheta$ one can…

We introduce a natural nondegeneracy condition for Poisson structures, called holonomicity, which is closely related to the notion of a log symplectic form. Holonomic Poisson manifolds are privileged by the fact that their deformation…

We establish cosection localization and vanishing results for virtual fundamental classes of derived manifolds, combining the theory of derived differential geometry by Joyce with the theory of cosection localization by Kiem-Li. As an…

We present the results of computation of cohomology for some Lie (super)algebras of Hamiltonian vector fields and related algebras. At present, the full cohomology rings for these algebras are not known even for the low dimensional vector…

In this paper we use invariant theory to develop the notion of cohomological detection for Type I classical Lie superalgebras. In particular we show that the cohomology with coefficients in an arbitrary module can be detected on smaller…

A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory…

We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative…

In this paper, we generalize all the results obtained on para-K\"ahler Lie algebras in Journal of Algebra {\bf 436} (2015) 61-101 to para-K\"ahler Lie algebroids. In particular, we study exact para-K\"ahler Lie algebroids as a…

We prove that the singular cohomology with finite coefficients of a finite-dimensional Stein space $S$ is isomorphic to the \'etale cohomology of the Stein algebra $\mathcal{O}(S)$. We deduce that any class in $H^k(S,\mathbb{Z})$ comes from…

Let X be a smooth algebraic variety over a field K containing the real numbers. We introduce the notion of twisted associative (resp. Poisson) deformation of the structure sheaf of X. These are stack-like versions of usual deformations. We…

Let M be a manifold and g a Lie algebra acting on M. Differential forms Omega(M) carry a natural action of Lie derivatives L(x) and contractions I(x) of fundamental vector fields for x \in g. Contractions (anti-) commute with each other,…

We develop a set of sufficient conditions for guaranteeing that an integrable system with a symmetry group $K$ on a manifold $M$ descends to an integrable system on a dense open subset of the quotient Poisson space $M/K$. The higher…

We propose an deepened analysis of KV-Poisson structures of on IR^2. We present their classification their properties an their possible applications in different domains. We prove that these structure give rise to a new Cohomological…

An infinite family of quasi-maximally superintegrable Hamiltonians with a common set of (2N-3) integrals of the motion is introduced. The integrability properties of all these Hamiltonians are shown to be a consequence of a hidden…

In this paper, we study invariant Poisson structures on homogeneous manifolds, which serve as a natural generalization of homogeneous symplectic manifolds previously explored in the literature. Our work begins by providing an algebraic…

The integral singular cohomology ring of the Grassmann variety parametrizing $r$-dimensional subspaces in the $n$-dimensional complex vector space is naturally an irreducible representation of the Lie algebra of all the $n\times n$ matrices…

For a compact Lie group G we define a regularized version of the Dolbeault cohomology of a G-equivariant holomorphic vector bundles over non-compact Kahler manifolds. The new cohomology is infinite-dimensional, but as a representation of G…

Let $\mathfrak g$ be a finite-dimensional Lie algebra. The symmetric algebra $\mathcal S(\mathfrak g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates…

It is known that the computation of the Poisson cohomology is closely related to the classification of singularities of Poisson structures. In this paper, we will first look for the normal forms of germs at (0,0) of Poisson structures on…