In this paper we find a certain solution of Poisson type fractional differential equation using theory tensor product Banach spaces.

Fix a manifold M , and let V be an infinite dimensional simple Lie subalgebra of the Lie algebra VecM of vector fields on M . Assume that V contains a finite dimensional simple maximal subalgebra a(V). We define an a(V)-quantization of a V-module of differential operators on M to be a decomposition of the module into irreducible a(V)-modules. In this article we survey some recent results and op...

Using a Poisson bracket representation, in 3D, of the Lie algebra 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 of the “kinetic energy”, related to the quadratic Casimir function. We then consider the potentials which can be added, whilst remaining integrable, leading to families ...

Coisotropic algebras are used to formalize coisotropic reduction in Poisson geometry as well deformation quantization and find applications various other fields well. In this paper we prove a Serre-Swan Theorem relating the regular projective modules over algebra built out of manifold $M$, submanifold $C$ an integrable smooth distribution $D \subseteq TC$ with vector bundles geometric situation...

In this paper we prove a conjecture of B. Shoikhet. This conjecture states that the tangent isomorphism on homology, between the Poisson homology associated to a Poisson structure on R d and the Hochschild homology of its quantized star-product algebra , is an isomorphism of modules over the (isomorphic) respective cohomology algebras. As a consequence, we obtain a version of the Duflo isomorph...

We investigate Poisson properties of Postnikov’s map from the space of edge weights of a planar directed network into the Grassmannian. We show that this map is Poisson if the space of edge weights is equipped with a representative of a 6-parameter family of universal quadratic Poisson brackets and the Grasmannian is viewed as a Poisson homogeneous space of the general linear group equipped wit...