Related papers: Noncommutative Networks on a Cylinder

We study one and two parameter quantizations of the function algebra on a semisimple orbit in the coadjoint representation of a simple Lie group subject to the condition that the multiplication on the quantized algebra is invariant under…

Let $A$ be a Koszul (or more generally, $N$-Koszul) Calabi-Yau algebra. Inspired by the works of Kontsevich, Ginzburg and Van den Bergh, we show that there is a derived non-commutative Poisson structure on $A$, which induces a graded Lie…

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…

We use compactifications of C*-algebras to introduce noncommutative coarse geometry. We transfer a noncommutative coarse structure on a C*-algebra with an action of a locally compact Abelian group by translations to Rieffel deformations and…

A.A. Kirillov introduced the family algebras in 2000. In this paper we study the noncommutative Poisson bracket P on the classical family algebra. We show that P is the first-order deformation from the classical family algebra to the…

In this paper, we present a theory of Poisson deformation of Hamiltonian quasi-Poisson manifolds to Hamiltonian Poisson manifolds that include degenerate cases. More significantly, this theory extends to singular cases arising from…

We derive a Hamiltonian structure for the $N$-particle hyperbolic spin Ruijsenaars-Schneider model by means of Poisson reduction of a suitable initial phase space. This phase space is realised as the direct product of the Heisenberg double…

To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X. If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson…

We consider a class of map, recently derived in the context of cluster mutation. In this paper we start with a brief review of the quiver context, but then move onto a discussion of a related Poisson bracket, along with the Poisson algebra…

The fully coupled dynamic interaction problem of the free surface of an incompressible fluid and a rigid body beneath it, in an inviscid, irrotational framework and in the absence of surface tension, is considered. Evolution equations of…

Let \Sigma_g be a closed orientable surface let Diff_0(\Sigma_g; area) be the identity component of the group of area-preserving diffeomorphisms of \Sigma_g. In this work we present an extension of Gambaudo-Ghys construction to the case of…

We examine the role of non-commutative geometry in D$p$-branes within large R-R field backgrounds. In this context, the background of a significant ($p-1$)-form R-R field can be effectively described using a ($p-1$)-bracket, similar to the…

We investigate a class of non-quasi-homogeneous free divisors in the sense of Saito. These divisors are defined by equations of the form $D:= \{h=0\}$ on $\mathbb{C}^p$, where the polynomial $h$ is specific linear combination of monomials…

We define a new basis of the algebra of quasi-symmetric functions by lifting the cycle-index polynomials of symmetric groups to noncommutative polynomials with coefficients in the algebra of free quasi-symmetric functions, and then…

Given a symplectic form and a pseudo-riemannian metric on a manifold, a non degenerate even Poisson bracket on the algebra of differential forms is defined and its properties are studied. A comparison with the Koszul-Schouten bracket is…

We introduce the notion of tropicalization for Poisson structures on $\mathbb{R}^n$ with coefficients in Laurent polynomials. To such a Poisson structure we associate a polyhedral cone and a constant Poisson bracket on this cone. There is a…

The semiclassical limit of full non-commutative gauge theory is known as Poisson gauge theory. In this work we revise the construction of Poisson gauge theory paying attention to the geometric meaning of the structures involved and advance…

An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson…

The Poisson gauge theory is a semi-classical limit of full non-commutative gauge theory. In this work we construct an L$_\infty^{full}$ algebra which governs both the action of gauge symmetries and the dynamics of the Poisson gauge theory.…

We construct a natural prequantization space over a monotone product of a toric manifold and an arbitrary number of complex Grassmannians of 2-planes in even-dimensional complex spaces, and prove that the universal cover of the identity…