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In the BRST quantization of gauge theories, the zero locus $Z_Q$ of the BRSTdifferential $Q$ carries an (anti)bracket whose parity is opposite to that ofthe fundamental bracket. We show that the on-shell BFV/BV gauge symmetries arein a 1:1 correspondence with Hamiltonian vector fields on $Z_Q$, andobservables of the BRST theory are in a 1:1 correspondence with characteristicfunctions of the bracket on $Z_Q$. By reduction to the zero locus, we obtainrelations between bracket operations and differentials arising in differentcomplexes (the Gerstenhaber, Schouten, Berezin-Kirillov, and Sklyaninbrackets); the equation ensuring the existence of a nilpotent vector field onthe reduced manifold can be the classical Yang-Baxter equation. We alsogeneralize our constructions to the bi-QP-manifolds which from the BRST theoryviewpoint corresponds to the BRST-anti-BRST-symmetric quantization.Comment: 21 pages, latex2e, several modifications have been made, main content  remains unchange

Becchi–Rouet–Stora–Tyutin formalism and zero locus reduction