  Lian and Zuckerman proved that the homology of a topological chiral algebra
can be equipped with the structure of a BV-algebra; \ie one can introduce a
multiplication, an odd bracket, and an odd operator $\Delta$ having the same
properties as the corresponding operations in Batalin-Vilkovisky quantization
procedure. We give a simple proof of their results and discuss a generalization
of these results to the non chiral case. To simplify our proofs we use the
following theorem giving a characterization of a BV-algebra in terms of
multiplication and an operator $\Delta$: {\em If $A$ is a supercommutative,
associative algebra and $\Delta$ is an odd second order derivation on $A$
satisfying $\Delta^2=0$, one can provide $A$ with the structure of a
BV-algebra.}
