  One may introduce at least three different Lie algebras in any Lagrangian
field theory : (i) the Lie algebra of local BRST cohomology classes equipped
with the odd Batalin-Vilkovisky antibracket, which has attracted considerable
interest recently~; (ii) the Lie algebra of local conserved currents equipped
with the Dickey bracket~; and (iii) the Lie algebra of conserved, integrated
charges equipped with the Poisson bracket. We show in this paper that the
subalgebra of (i) in ghost number $-1$ and the other two algebras are
isomorphic for a field theory without gauge invariance. We also prove that, in
the presence of a gauge freedom, (ii) is still isomorphic to the subalgebra of
(i) in ghost number $-1$, while (iii) is isomorphic to the quotient of (ii) by
the ideal of currents without charge. In ghost number different from $-1$, a
more detailed analysis of the local BRST cohomology classes in the Hamiltonian
formalism allows one to prove an isomorphism theorem between the antibracket
and the extended Poisson bracket of Batalin, Fradkin and Vilkovisky.
