Another possibility is to use something other than the tensor algebra as the covering algebra. One such possibility is to use the exterior algebra; that is, to replace every occurrence of the tensor product by the exterior product. If the base algebra is a Lie algebra, then the result is the Gerstenhaber algebra; it is the exterior algebra of the corresponding Lie group. As before, it has a grading naturally coming from the grading on the exterior algebra. (The Gerstenhaber algebra should not be confused with the Poisson superalgebra; both invoke anticommutation, but in different ways.)