Abstract

The fundamental example of Gerstenhaber algebra is the space T poly ( R d ) of polyvector fields on R d , equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping G ∞ algebra of a Gerstenhaber algebra G . This structure gives us a definition of the Chevalley–Harrison cohomology operator for G . We finally show the nontriviality of a Chevalley–Harrison cohomology group for a natural Gerstenhaber subalgebra in T poly ( R d ) .

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