Abstract
Let us consider a Lie (super)algebra G spanned by Tα where Tα are quantum observables in BV formalism. It is proved that for every tensor cα...α that determines a homology class of the Lie algebra G the expression cα...αTα...Tα is again a quantum observable. This theorem is used to construct quantum observables in the BV sigma model. We apply this construction to explain Kontsevich's results about the relation between homology of the Lie algebra of Hamiltonian vector fields and topological invariants of manifolds.
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