Simple Finite Jordan Pseudoalgebras

We consider the structure of Jordan $H$-pseudoalgebras which are linearly finitely generated over a Hopf algebra $H$. There are two cases under consideration: $H=U(\mathfrak{h})$ and H=U(\mathfrak h)# \mathbb C[\Gamma ], where $\mathfrak{h}$ is a finite-dimensional Lie algebra over $\mathbb{C}$, $\mathrm{\Gamma }$ is an arbitrary group acting on $U(\mathfrak{h})$ by automorphisms. We construct an analogue of the Tits-Kantor-Koecher construction for finite Jordan pseudoalgebras and describe all simple ones.