2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74780A realization of coherent state Lie algebras by first-order differential operators with holomorphic polynomial coefficients on Kähler coherent state orbits is presented. Explicit formulas involving the Bernoulli numbers and the structure constants for the semisimple Lie groups are proved.26 pages, AMSART, AMS fonts, to appear in the Proceedings of the International Conference ``Operator Algebras and Mathematical Physics'', June 26 - July 04, 2003, Sinaia, RomaniaDifferential GeometryMathematical Physics81R30; 22E46; 32WXXtext