Related papers: Polyubles, Poisson homogeneous spaces and multi-fl…

We construct modular spaces of all 6-dimensional real semisimple Drinfeld doubles, i.e. the sets of all possible decompositions of the Lie algebra of the Drinfeld double into Manin triples. These modular spaces are significantly different…

We construct explicitly a class of coboundary Poisson-Lie structures on the group of formal diffeomorphisms of ${\Bbb R}^n$. Equivalently, these give rise to a class of coboundary triangular Lie bialgebra structures on the Lie algebra $W_n$…

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…

In analogy to the KP theory, the second Poisson structure for the dispersionless KP hierarchy can be defined on the space of commutative pseudodifferential operators $L=p^n+\sum_{j=-\infty}^{n-1}u_j p^j$. The reduction of the Poisson…

There is a well-established procedure of assigning a strong homotopy Lie algebra of local observables to a multisymplectic manifold which can be regarded as part of a categorified Poisson structure. For a 2-plectic manifold, the resulting…

We provide a coarse classification of all 8-dimensional Manin triples, that describe Poisson--Lie T-dualities between 4-dimensional group manifold solutions to supergravity equations. We find several such dualities and one Poisson--Lie…

Automorphism, isomorphism, and embedding problems are investigated for a family of Nambu-Poisson algebras (or $n$-Lie Poisson algebras) using Poisson valuations.

To each polynomial $\v\in\F[x,y,z]$ is associated a Poisson structure on $\F^3$, a surface and a Poisson structure on this surface. When $\v$ is weight homogeneous with an isolated singularity, we determine the Poisson cohomology and…

In this paper, we give a description of holomorphic multi-vector fields on smooth compact toric varieties, which generalizes Demazure's result of holomorphic vector fields on toric varieties. Based on the result, we compute the Poisson…

We present a general definition of the Poisson bracket between differential forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories and, more generally, on exact multisymplectic…

Let G be a compact Lie group or a complex reductive affine algebraic group. We explore induced mappings between G-character varieties of surface groups by mappings between corresponding surfaces. It is shown that these mappings are…

We compute the Poisson cohomology of the linear Poisson structure dual to the n-dimensional "book" Lie algebra, defined by [e_0,e_i]=e_i, [e_i,e_j]=0, for i,j=1,...,n-1.

This paper consists of two parts. In the first part we show that any Poisson algebraic group over a field of characteristic zero and any Poisson Lie group admits a local quantization. This answers positively a question of Drinfeld. In the…

We study invariants and structures of Poisson fields of rational functions in two variables. For four particular families, we classify the members, establish criteria for isomorphisms and, with the exception of the Weyl Poisson field,…

We first extend the notion of connection in the context of Courant algebroids to obtain a new characterization of generalized Kaehler geometry. We then establish a new notion of isomorphism between holomorphic Poisson manifolds, which is…

A Manin triples (D; g; ~ g) is a bialgebra (g; ~ g which don't intersect each others and a direct sum of this bialgebra D = g ~ g). If the corresponding Lie groups have a Poisson structure, they are called Poisson-Lie groups. A Poisson-Lie…

This paper is intended both an introduction to the algebraic geometry of holomorphic Poisson brackets, and as a survey of results on the classification of projective Poisson manifolds that have been obtained in the past twenty years. It is…

Four-dimensional Manin triples and Drinfeld doubles are classified and corresponding two-dimensional Poisson-Lie T-dual sigma models on them are constructed. The simplest example of a Drinfeld double allowing decomposition into two…

We compute the Poisson cohomology associated with several three dimensional Lie algebras. Together with existing results and the classification of three dimensional Lie algebras, this provides the Poisson cohomology of all linear Poisson…

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…