Related papers: On a Poisson-algebraic characterization of vector …

We prove that the Lie algebra $\mathcal{S}(\mathcal{P}(E,M))$ of symbols of linear operators acting on smooth sections of a vector bundle $E\to M,$ characterizes it. To obtain this, we assume that $\mathcal{S}(\mathcal{P}(E,M))$ is seen as…

We prove a Lie-algebraic characterization of vector bundle for the Lie algebra $\mathcal{D}(E,M),$ seen as ${\rm C}^\infty(M)-$module, of all linear operators acting on sections of a vector bundle $E\to M$. We obtain similar result for its…

We prove that a vector bundle $\pi : E \to M$ is characterized by the Lie algebra generated by all differential operators on $E$ which are eigenvectors of the Lie derivative in the direction of the Euler vector field. Our result is of…

We prove that a vector bundle $ E \to M$ is characterized by the associative structure of the space of symbols of the Lie algebra generated by all differential operators on $E$ which are eigenvectors of the Lie derivative in the direction…

In this paper we construct a Poisson algebra bundle whose distributional sections are suitable to represent multilocal observables in classical field theory. To do this, we work with vector bundles over the unordered configuration space of…

We study equivariant vector bundles over configuration spaces with diagonals included, viewed as orbifold quotients $M^n/\mathfrak{S}_n$ by permutation groups. Working in the equivalent language of equivariant vector bundles, we construct…

We prove Pursell-Shanks type results for the Lie algebra D(M) of all linear differential operators of a smooth manifold M, for its Lie subalgebra D^1(M) of all linear first-order differential operators of M, and for the Poisson algebra…

Let $P$ be a Poisson algebra with a Lie bracket $\{, \}$ over a field $\F$ of characteristic $p\geq 0$. In this paper, the Lie structure of $P$ is investigated. In particular, if $P$ is solvable with respect to its Lie bracket, then we…

We introduce the \emph{universal algebra} of two Poisson algebras $P$ and $Q$ as a commutative algebra $A:={\mathcal P} (P, \, Q )$ satisfying a certain universal property. The universal algebra is shown to exist for any finite dimensional…

Let $X$ be a complex irreducible smooth projective curve, and let ${\mathbb L}$ be an algebraic line bundle on $X$ with a nonzero section $\sigma_0$. Let $\mathcal{M}$ denote the moduli space of stable Hitchin pairs $(E,\, \theta)$, where…

Let G be a simple linear algebraic group defined over the complex numbers. Fix a proper parabolic subgroup P of G and a nontrivial antidominant character \chi of P. We prove that a holomorphic principal G-bundle E over a connected complex…

Results on derivations and automorphisms of some quantum and classical Poisson algebras, as well as characterizations of manifolds by the Lie structure of such algebras, are revisited and extended. We prove in particular somehow unexpected…

Let $G$ be a locally semisimple ind-group, $P$ be a parabolic subgroup, and $E$ be a finite-dimensional $P$-module. We show that, under a certain condition on $E$, the nonzero cohomologies of the homogeneous vector bundle…

In this paper we classify and construct differential symmetry breaking operators $\mathbb{D}$ from a line bundle over the real projective space $\mathbb{R}\mathbb{P}^n$ to a vector bundle over $\mathbb{R}\mathbb{P}^{n-1}$. We further…

We prove that for a vector bundle $ E \to M$, the Lie algebra $\mathcal{D}_{\mathcal{E}}(E)$ generated by all differential operators on $E$ which are eigenvectors of $L_{\mathcal{E}},$ the Lie derivative in the direction of the Euler vector…

We construct the family of algebroid brackets $[\cdot,\cdot]_{c,v}$ on the tangent bundle $T^*M$ to a Poisson manifold $(M,\pi)$ starting from an algebroid bracket of differential forms. We use these brackets to generate Poisson structures…

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 study noncommutative generalizations of such notions of the classical symplectic geometry as degenerate Poisson structure, Poisson submanifold and quotient manifold, symplectic foliation and symplectic leaf for associative Poisson…

We show that for every vector bundle E over any given symplectic manifold M there exists an explicitly given super-Poisson bracket on the space of sections of the dual Grassmann bundle associated to E built out of symplectic structure of M,…

Let G be a split semi-simple adjoint group, and S a colored decorated surface, given by an oriented surface with punctures, special boundary points, and a specified collection of boundary intervals. We introduce a moduli space P(G,S)…