Related papers: Bott-Samelson varieties and Poisson Ore extensions

We propose a new approach to building log-canonical coordinate charts for any simply-connected simple Lie group $\G$ and arbitrary Poisson-homogeneous bracket on $\G$ associated with Belavin--Drinfeld data. Given a pair of representatives…

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 develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp.…

We propose a simple approach to formal deformations of associative algebras. It exploits the machinery of multiplicative coresolutions of an associative algebra A in the category of A-bimodules. Specifically, we show that certain…

We study the algebraic structure of the Poisson algebra P(O) of polynomials on a coadjoint orbit O of a semisimple Lie algebra. We prove that P(O) splits into a direct sum of its center and its derived ideal. We also show that P(O) is…

We present a way to associate an algebra $B_G (\Upsilon) $ with every pseudo reflection group $G$. When $G$ is a Coxeter group of simply-laced type we show $B_G (\Upsilon)$ is isomorphic to the generalized Brauer algebra of simply-laced…

We develop a framework for Poisson geometry on loop spaces of low regularity, extending Mokhov's classical constructions from smooth loops to weak Sobolev spaces $W^{s,p}(\mathbb{S^1},\mathbb{R}^m)$ with $o < s \frac{1}{2}$ and $1 < p <…

We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…

Poisson structures vanishing linearly on a set of smooth closed disjoint curves are generic in the set of all Poisson structures on a compact connected oriented surface. We construct a complete set of invariants classifying these structures…

Symmetrical top is a special case of a general top. The canonical Poisson structure on T*SE(3) is the common method of its description. This Poisson structure is invariant under the right action of SO(3). However the Hamiltonian of the…

Given a Poisson structure (or, equivalently, a Hamiltonian operator) $P$, we show that its Lie derivative $L_{\tau}(P)$ along a vector field $\tau$ defines another Poisson structure, which is automatically compatible with $P$, if and only…

Motivated by the Poisson Dixmier-Moeglin equivalence problem, a systematic study of commutative unitary rings equipped with a {\em biderivation}, namely a binary operation that is a derivation in each argument, is here begun, with an eye…

The Poisson bracket algebra corresponding to the second Hamiltonian structure of a large class of generalized KdV and mKdV integrable hierarchies is carefully analysed. These algebras are known to have conformal properties, and their…

Crawley-Boevey introduced the definition of a noncommutative Poisson structure on an associative algebra A that extends the notion of the usual Poisson bracket. Let V be a symplectic manifold and G be a finite group of symplectimorphisms of…

We introduce a new 2-parameter family of sigma models exhibiting Poisson-Lie T-duality on a quasitriangular Poisson-Lie group $G$. The models contain previously known models as well as a new 1-parameter line of models having the novel…

The purpose of this work is to study Lie superalgebroid structures on the space of superdifferential $1$-forms over the supermanifolds whose superfunctions are the differential forms on its underlying manifold. These superalgbroids are…

We study a large class of Poisson manifolds, derived from Manin triples, for which we construct explicit partitions into regular Poisson submanifolds by intersecting certain group orbits. Examples include all varieties ${\mathcal L}$ of…

The purpose of this paper is to study covariant Poisson structures on the complex Grassmannian obtained as quotients by coisotropic subgroups of the standard Poisson--Lie SU(n). Properties of Poisson quotients allow to describe Poisson…

We give the 3-dimensional Sklyanin algebras $S$ that are module-finite over their center $Z$ the structure of a Poisson $Z$-order (in the sense of Brown-Gordon). We show that the induced Poisson bracket on $Z$ is non-vanishing and is…

We introduce a notion of weakly log-canonical Poisson structures on positive varieties with potentials. Such a Poisson structure is log-canonical up to terms dominated by the potential. To a compatible real form of a weakly log-canonical…