Related papers: Scheme-theoretic coisotropic reduction
This work introduces a unified approach to the reduction of Poisson manifolds using their description by graded symplectic manifolds. This yields a generalization of the classical Poisson reduction by distributions (Marsden-Ratiu…
The ``classical BRST construction'' as developed by Batalin-Fradkin-Vilkovisky is a homological construction for the reduction of the Poisson algebra $P = C^\infty (W)$ of smooth functions on a Poisson manifold $W$ by the ideal $I$ of…
We generalize various symplectic reduction techniques to the context of the optimal momentum map. Our approach allows the construction of symplectic point and orbit reduced spaces purely within the Poisson category under hypotheses that do…
We point out, and draw some consequences of, the fact that the Poisson Lie group G* dual to G=GL_n(C) (with its standard complex Poisson structure) may be identified with a certain moduli space of meromorphic connections on the unit disc…
Following Serre's initial work, a number of authors have considered twists of quadratic forms on a scheme Y by torsors of a finite group G, together with formulas for the Hasse-Witt invariants of the twisted form. In this paper we take the…
We study a generalized scheme of Swanson Hamiltonian from a second-derivative pseudosupersymmetric approach. We discuss plausible choices of the underlying quasi-Hamiltonian and consider the viability of applications to systems like the…
The imploded cross-section of a symplectic manifold is a stratified space allowing for an abelianization of its symplectic reduction. After recalling symplectic and Poisson reduction and reviewing the basics of symplectic implosion, we…
We show that the symplectic contraction map of Hilgert-Manon-Martens -- a symplectic version of Popov's horospherical contraction -- is simply the quotient of a Hamiltonian manifold $M$ by a "stratified null foliation" that is determined by…
The question studied here is the behavior of the Poisson bracket under C^0-perturbations. In this purpose, we introduce the notion of pseudo-representation and prove that for a normed Lie algebra, it converges to a representation. An…
Given a foliation S of a manifold M, a distribution Z in M transveral to S and a Poisson bivector \Pi on M we present a geometric method of reducing this operator on the foliation S along the distribution Z. It encompasses the classical…
It has been a long standing question how to extend the canonical Poisson bracket formulation from classical mechanics to classical field theories, in a completely general, intrinsic, and canonical way. In this paper, we provide an answer to…
We develop the theory of algebraic groups over real closed fields and apply the results to construct a geometric object $\mathcal{B}$ and to prove that $\mathcal{B}$ is an affine $\Lambda$-building. We use a model theoretic transfer…
We study the Poisson structure associated to the defocusing Ablowitz-Ladik equation from a functional-analytical point of view, by reexpressing the Poisson bracket in terms of the associated Caratheodory function. Using this expression, we…
In this work we study the integrability of quotients of quasi-Poisson manifolds. Our approach allows us to put several classical results about the integrability of Poisson quotients in a common framework. By categorifying one of the already…
Starting with a Lie algebroid ${\cal A}$ over a space $M$ we lift its action to the canonical transformations on the affine bundle ${\cal R}$ over the cotangent bundle $T^*M$. Such lifts are classified by the first cohomology $H^1({\cal…
Motivated by a conjecture that doubled four-dimensional Chern-Simons produces new integrable models, we perform its Hamiltonian analysis and find the theory's Poisson algebra. This requires carefully accounting for a set of boundary…
We give the analogue for Hopf algebras of the polyuble Lie bialgebra construction by Fock and Rosli. By applying this construction to the Drinfeld-Jimbo quantum group, we obtain a deformation quantization $\mathbb{C}_\hslash[(N \backslash…
In the first part of the paper we introduce some geometric tools needed to describe slow-fast Hamiltonian systems on smooth manifolds. We start with a smooth Poisson bundle $p: M\to B$ of a regular (i.e. of constant rank) Poisson manifold…
For a valuation ring $V$, a smooth $V$-algebra $A$, and a reductive $V$-group scheme $G$ satisfying a certain natural isotropicity condition, we prove that every Nisnevich $G$-torsor on $\mathbb{A}^N_A$ descends to a $G$-torsor on $A$. As a…
In this paper we study the isomonodromic deformations of systems of differential equations with poles of any order on the Riemann sphere as Hamiltonian flows on the product of co-adjoint orbits of the Takiff algebra (i.e. truncated current…