A representation of the Jacobi algebra by first order differential operators with polynomial coeficients on a Kähler manifold which as set is the product of the complex multidimensional plane times the Siegel ball is presented.
Stefan Berceanu. "A Holomorphic Representation of the Semidirect Sum of Symplectic and Heisenberg Lie Algebras." J. Geom. Symmetry Phys. 5 5 - 13, 2006. https://doi.org/10.7546/jgsp-5-2006-5-13