Related papers: Poisson structures on almost complex Lie algebroid…

The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost…

We describe transposed Poisson structures on the upper triangular matrix Lie algebra $T_n(F)$, $n>1$, over a field $F$ of characteristic zero. We prove that, for $n>2$, any such structure is either of Poisson type or the orthogonal sum of a…

There are studied Lie groups considered as almost hypercomplex Hermitian-Norden manifolds, which are integrable and have the lowest dimension four. It is established a correspondence of the derived Lie algebras of types of invariant…

We define Poisson structures on certain transversal slices to conjugacy classes in complex simple algebraic groups introduced in arXiv:0809.0205. These slices are associated to the elements of the Weyl group, and the Poisson structures on…

We study a modification of Poisson geometry by a closed 3-form. Just as for ordinary Poisson structures, these "twisted" Poisson structures are conveniently described as Dirac structures in suitable Courant algebroids. The additive group of…

In this work, the complex Lie affgebra structures on three-dimensional solvable Lie algebras are completely determined.

Generalised almost complex structures $\mathcal J$ on transitive Courant algebroids $E$ are studied in terms of their components with respect to a splitting $E\cong TM \oplus T^*M \oplus \mathcal G$, where $M$ denotes the base of $E$ and…

We present an algebraic framework for the computation of low-degree cohomology of a class of bigraded complexes which arise in Poisson geometry around (pre)symplectic leaves. We also show that this framework can be applied to the more…

In this paper, firstly, for some $4n$-dimensional almost complex manifolds $M_{i}, ~1\le i \le \alpha$, we prove that $\left(\sharp_{i=1}^{\alpha} M_{i}\right) \sharp (\alpha{-}1) \mathbb{C} P^{2n}$ must admits an almost complex structure,…

In this note we construct a canonical lifting of arbitrary Poisson structures on a manifold to its algbera of densities. Using this construction we proceed to classify all extensions of a fixed structure on the original manifold to its…

Double (quasi-)Poisson brackets were introduced on associative algebras by Van den Bergh to induce a (quasi-)Poisson structure on their representation spaces naturally equipped with a $\mathrm{GL}$-action (type $\mathtt{A}$). If there…

The object of investigations are almost hypercomplex structures with Hermitian-Norden metrics on 4-dimensional Lie groups considered as smooth manifolds. There are studied both the basic classes of a classification of 4-dimensional…

The concept of Poisson cohomology groups associated with Poisson manifolds is a part of the theory of Lie superalgebras of vector fields. Therefore, we abstracted them as Poisson-like cohomology groups for general Lie superalgebras. In…

The subject for investigation in this note is concerned with holomorphic Poisson structures on nilmanifolds with abelian complex structures. As a basic fact, we establish that on such manifolds, the Dolbeault cohomology with coefficients in…

We give the extension formulae on almost complex manifolds and give decompositions of the extension formulae. As applications, we study $(n,0)$-forms, the $(n,0)$-Dolbeault cohomology group and $(n,q)$-forms on almost complex manifolds.

We connect Poisson and near-symplectic geometry by showing that there is a singular Poisson structure on a near-symplectic 4-manifold. The Poisson structure $\pi$ is defined on the tubular neighbourhood of the singular locus $Z_{\omega}$ of…

We construct a corank one Poisson manifold which is of strong compact type, i.e., the associated Lie algebroid structure on its cotangent bundle is integrable, annd the source 1-conected (symplectic) integration is compact. The construction…

The existence of quasi-bi-Hamiltonian structures for the Kepler problem is studied. We first relate the superintegrability of the system with the existence of two complex functions endowed with very interesting Poisson bracket properties…

In the present paper we explicitly construct deformation quantizations of certain Poisson structures on E^*, where E -> M is a Lie algebroid. Although the considered Poisson structures in general are far from being regular or even…

We introduce a notion of a weak Poisson structure on a manifold $M$ modeled on a locally convex space. This is done by specifying a Poisson bracket on a subalgebra $\cA \subeq C^\infty(M)$ which has to satisfy a non-degeneracy condition…