Abstract: The fundamental example of Gerstenhaber algebra is the space of polyvector fields on , equipped with the wedge product and the Schouten bracket. In this paper, we explicitely describe what is the enveloping algebra of a Gerstenhaber algebra . This structure gives us a definition of the Chevalley–Harrison cohomology operator for . We finally show the nontriviality of a Chevalley–Harrison cohomology group for a natural Gerstenhaber subalgebra in . [Copyright &y& Elsevier]