BECCHI-ROUET-STORA-TYUTIN STRUCTURE OF POLYNOMIAL POISSON ALGEBRAS

The Becchi-Rouet-Stora-Tyutin (BRST) structure of polynomial Poisson a lgebras is investigated. It is shown that Poisson algebras provide non trivial models where the full BRST recursive procedure is needed. Quad ratic Poisson algebras may already be of arbitrarily high rank. Explic it examples are provided, for which the first terms of the BRST genera tor are given. The calculations are cumbersome but purely algorithmic, and have been treated by means of the computer algebra system REDUCE. Our analysis is classical (=nonquantum) throughout.