Superalgebra structure on differential forms of manifold

Abstract

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.

26 pages

References in corpus (3)

• Cohomology groups of homogeneous Poisson structures
• Euler number and Betti numbers of homology groups of pre Lie superalgebra
• Super homologies associated with low dimensional Lie algebras