Related papers: The Fock-Rosly Poisson Structure as Defined by a Q…

We review nonabelian Poisson structures on affine and projective spaces over $\mathbb{C}$. We also construct a class of examples of nonabelian Poisson structures on $\mathbb{C} P^{n-1}$ for $n>2$. These nonabelian Poisson structures depend…

The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized…

In this paper, generalizing the construction of \cite{HP1}, we equip the relative moduli stack of complexes over a Calabi-Yau fibration (possibly with singular fibers) with a shifted Poisson structure. Applying this construction to the…

We are interested in analytic singular Poisson structures with a non zero linear part at the singularity. Using recent work of the author about holomorphic normalization of commutative familly of singular vector fields, we obtain results…

In a recent work, we constructed a rational map from a simple Lie group $\mathcal G$ to itself that intertwines the standard Poisson--Lie structure on $\mathcal G$ with a Poisson homogeneous one defined by a pair of quasi-triangular…

We investigate conformal relative equilibria for Hamiltonian systems on exact Poisson manifolds equipped with scaling symmetries. By introducing conformally Poisson actions and conformal momentum maps, we characterize these equilibria…

In this paper, we investigate pre-Calabi-Yau algebras and homotopy double Poisson algebras arising from homotopy Rota-Baxter structures. We introduce the notion of cyclic homotopy Rota-Baxter algebras, a class of homotopy Rota-Baxter…

Lie bialgebra structures are reviewed and investigated in terms of the double Lie algebra, of Manin- and Gau{\ss}-decompositions. The standard R-matrix in a Manin decomposition then gives rise to several Poisson structures on the…

After a brief summary of the main properties of Poisson manifolds and Lie algebroids in general, we survey recent work on the modular classes of Poisson and twisted Poisson manifolds, of Lie algebroids with a Poisson or twisted Poisson…

We show that relative Calabi--Yau structures on noncommutative moment maps give rise to (quasi-)bisymplectic structures, as introduced by Crawley-Boevey-Etingof-Ginzburg (in the additive case) and Van den Bergh (in the multiplicative case).…

As a generalization of Postnikov's construction (see arXiv: math/0609764), we define a map from the space of edge weights of a directed network in an annulus into a space of loops in the Grassmannian. We then show that universal Poisson…

We give an $L_\infty$-interpretation of the classification, obtained in [AP2], of the formal deformations of a family of exact Poisson structures in dimension three. We indeed obtain again the explicit formulas for all the formal…

In this paper a double quasi Poisson bracket in the sense of Van den Bergh is constructed on the space of noncommutative weights of arcs of a directed graph embedded in a disk or cylinder $\Sigma$, which gives rise to the quasi Poisson…

We prove a rigidity theorem for the Poisson automorphisms of the function fields of tori with quadratic Poisson structures over fields of characteristic 0. It gives an effective method for classifying the full Poisson automorphism groups of…

We describe a deformation quantization of a modification of Poisson geometry by a closed 3-form. Under suitable conditions it gives rise to a stack of algebras. The basic object used for this aim is a kind of families of Poisson structures…

The paper is devoted to quadratic Poisson structures compatible with the canonical linear Poisson structures on trivial 1-dimensional central extensions of semisimple Lie algebras. In particular, we develop the general theory of such…

Let $\g$ be a finite dimensional complex Lie algebra and $\l\subset \g$ a Lie subalgebra equipped with the structure of a factorizable quasitriangular Lie bialgebra. Consider the Lie group $\Exp \l$ with the Semenov-Tjan-Shansky Poisson…

We show that for any coboundary Poisson Lie group G, the Poisson structure on G^* is linearizable at the group unit. This strengthens a result of Enriquez-Etingof-Marshall, who had established formal linearizability of G^* for…

We exhibit new examples of double quasi-Poisson brackets, based on some classification results and the method of fusion. This method was introduced by Van den Bergh for a large class of double quasi-Poisson brackets which are said…

In our recent paper we proved the polynomiality of a Poisson bracket for a class of infinite-dimensional Hamiltonian systems of PDE's associated to semi-simple Frobenius structures. In the conformal (homogeneous) case, these systems are…