  As an analogy of superalgebra of multivector fields with the Schounte
bracket, we introduce a non-trivial superbracket on differential forms of
manifold. We show properties of this new superalgebra. We extend this
superalgebra by adding one factor. The new extended superalgebra should be
studied more widely and in deep. We study Betti numbers of double weighted
homology groups by the Euler vector field. In appendix, we explain our bracket
is produced like as the Schouten bracket.

General Mathematics