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 $\mathbb C$, $\Gamma$ 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.