Superalgebra structure on differential forms of manifold

TL;DR

This paper introduces a novel superbracket on differential forms of manifolds, extending superalgebra structures and exploring their properties, with implications for homology and connections to the Schouten bracket.

Contribution

It presents a new superbracket on differential forms, extending existing superalgebra structures and analyzing their properties and homological implications.

Findings

Defined a new superbracket analogous to the Schouten bracket.

Extended the superalgebra by adding an extra factor.

Analyzed Betti numbers of double weighted homology groups.

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.