Related papers: Ultralocal Lax connection for para-complex $\mathb…

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 derive the $2$d Zakharov-Mikhailov action from $4$d Chern-Simons theory. This $2$d action is known to produce as equations of motion the flatness condition of a large class of Lax connections of Zakharov-Shabat type, which includes an…

We introduce a family of loop soup models on the hypercubic lattice. The models involve links on the edges, and random pairings of the link endpoints on the sites. We conjecture that loop correlations of distant points are given by…

Preliminary results toward the analysis of the Hamiltonian structure of multifield theories describing complex materials are mustered: we involve the invariance under the action of a general Lie group of the balance of substructural…

We introduce a natural class of multicomponent local Poisson structures $\mathcal P_k + \mathcal P_1$, where $\mathcal P_1$ is a local Poisson bracket of order one and $\mathcal P_k$ is a homogeneous Poisson bracket of odd order $k$ under…

This paper is devoted to the study of the Hamiltonian formulation of non-linear sigma models on supercoset targets. We calculate the Poisson brackets of left-invariant currents. Then we introduce the Hamiltonian of the system and determine…

There is constructed a family of Lie algebras that act in a Hamiltonian way on the symplectic affine space of linear symplectic connections on a symplectic manifold. The associated equivariant moment map is a formal sum of the Cahen-Gutt…

Let $G$ be a connected Lie group and $\mathfrak{g}$ its Lie algebra. We denote by $\nabla^0$ the torsion free bi-invariant linear connection on $G$ given by $\nabla^0_XY=\frac12[X,Y],$ for any left invariant vector fields $X,Y$. A Poisson…

Using a Poisson bracket representation, in 3D, of the Lie algebra $\mathfrak{sl}(2)$, we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras…

Poisson brackets between conserved quantities are a fundamental tool in the theory of integrable systems. The subclass of weakly nonlocal Poisson brackets occurs in many significant integrable systems. Proving that a weakly nonlocal…

We construct an analogue of Dirac's reduction for an arbitrary local or non-local Poisson bracket in the general setup of non-local Poisson vertex algebras. This leads to Dirac's reduction of an arbitrary non-local Poisson structure. We…

Reversible part of evolution equations of physical systems is often generated by a Poisson bracket. We discuss geometric means of construction of Poisson brackets and their mutual coupling (direct, semidirect and matched-pair products) as…

The goal of this paper is to develop the theory of Courant algebroids with integrable para-Hermitian vector bundle structures by invoking the theory of Lie bialgebroids. We consider the case where the underlying manifold has an almost…

A common approach to the theory of nonlocal Poisson brackets, seen from the operatorial point of view, has been to keep implicit the sets on which these brackets act. In this paper we aim to explicitly define appropriate functional spaces…

The link between (super)-affine Lie algebras as Poisson brackets structures and integrable hierarchies provides both a classification and a tool for obtaining superintegrable hierarchies. The lack of a fully systematic procedure for…

We study Poisson symmetric spaces of group type with Cartan subalgebra "adapted" to the Lie cobracket.

Some applications of the odd Poisson bracket developed by Kharkov's theorists are represented, including the reformulation of classical Hamiltonian dynamics, the description of hydrodynamics as a Hamilton system by means of the odd bracket…

Gauged linear sigma models with (0,2) supersymmetry allow a larger choice of couplings than models with (2,2) supersymmetry. We use this freedom to find a fully linear construction of torsional heterotic compactifications, including models…

We revisit and construct new examples of supersymmetric 2D topological sigma models whose target space is a Poisson supermanifold. Inspired by the AKSZ construction of topological field theories, we follow a graded-geometric approach and…

We prove an equivariant version of the local splitting theorem for tame Poisson structures and Poisson actions of compact Lie groups. As a consequence, we obtain an equivariant linearization result for Poisson structures whose transverse…