Related papers: Transverse Poisson Structures to Adjoint orbits in…

The main purpose of the paper is to study hyperkahler structures from the viewpoint of symplectic geometry. We introduce a notion of hypersymplectic structures which encompasses that of hyperkahler structures. Motivated by the work of…

The aim of this paper is to introduce the notion of (noncommutative) transposed Poisson conformal algebras, which serve as the conformal analogues of transposed Poisson algebras and admit a rich class of identities. We show that the tensor…

We introduce the notion of a $\theta$-almost twisted Poisson structure on manifolds, which involves incorporating a closed $1$-form $\theta$ into twisted Poisson structures under specific conditions. We provide a characterization of this…

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…

In this paper, we introduce the definition of transposed Novikov-Poisson algebras, whose affinization are transposed Poisson algebras. Moreover, we show that there is a natural transposed Poisson algebra structure on the tensor product of a…

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 classify in this paper Poisson structures on modules over semisimple Lie algebras arising from classical r-matrices. We then study their quantizations and the relation to classical invariant theory.

In this paper we study associative algebras with a Poisson algebra structure on the center acting by derivations on the rest of the algebra. These structures, which we call Poisson fibred algebras, appear in the study of quantum groups at…

We prove that the classical $W$-algebra associated to a nilpotent orbit in a simple Lie-algebra can be constructed by preforming bihamiltonian, Drinfeld-Sokolov or Dirac reductions. We conclude that the classical $W$-algebra depends only on…

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…

We study {\em right-invariant (resp., left-invariant) Poisson quasi-Nijenhuis structures} on a Lie group $G$ and introduce their infinitesimal counterpart, the so-called {\em r-qn structures} on the corresponding Lie algebra $\mathfrak g$.…

We propose a systematic and topological study of limits $\lim_{\nu\to 0^+}G_\mathbb{R}\cdot(\nu x)$ of continuous families of adjoint orbits for non-compact simple Lie groups. This limit is always a finite union of nilpotent orbits. We…

This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent…

Let G be a Lie group and g its Lie algebra. We develop a theory of quasi Poisson structures relative to a not necessarily non-degenerate Ad-invariant symmetric 2-tensor in the tensor square of g and one of general not necessarily…

Recantly, William Crawley-Boevey proposed the definition of a Poisson structure on a noncommutative algebra $A$ based on the Kontsevich principle. His idea was to find the {\it weakest} possible structure on $A$ that induces standard…

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…

We study the equivalence of Poisson structures around a given symplectic leaf of nonzero dimension. Some criteria of Poisson equivalence are derived from a homotopy argument for coupling Poisson structures. In the case when the transverse…

We construct families of functions in involution for transverse Poisson structures at nilpotent elements of Lie-Poisson structures on simple Lie algebras by using the argument shift method. Examples show that these families contain…

Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the…

A Poisson structure on a manifold is characterized by the Schouten bracket. The graded algebra of the tangent bundle with the Schouten bracket is a prototype of Lie superalgebra. The Poisson condition means that a cycle in the 2-chain…