Euler number and Betti numbers of homology groups of pre Lie superalgebra

Abstract: First we recall homology groups of prer Lie superalgebras. Then introducing double weighted chain spaces, we deal with pre Lie superalgebra of multi-vector fields with polynomial coefficients on n-dimensional number space. The bracket is Schouten bracket. We have several results about Euler number and Betti numbers of those homology groups of special pre Lie superalgebra.