THE SH LIE-STRUCTURE OF POISSON BRACKETS IN-FIELD THEORY

A general construction of an sh Lie algebra (L-infinity-algebra) from a homological resolution of a Lie algebra is given. It is applied to t he space of local functionals equipped with a Poisson bracket, induced by a bracket for local functions along the lines suggested by Gel'fan d, Dickey and Dorfman. In this way, higher order maps are constructed which combine to form an sh Lie algebra on the graded differential alg ebra of horizontal forms. The same construction applies for graded bra ckets in field theory such as the Batalin-Fradkin-Vilkovisky bracket o f the Hamiltonian BRST theory or the Batalin-Vilkovisky antibracket.