Superalgebra structure on differential forms of manifold

2021/05/14 by Kentaro Mikami, Mikami, Kentaro, Tadayoshi Mizutani +1 · 1 citation
Mathematics · #53Dxx #81S10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #General Mathematics (math.GM) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2105.09738

openalex publication_date 2021/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Super homology groups of differential forms and vector fields on Euclidean line

Related

• Super homology groups of differential forms and vector fields on Euclidean line
• Super homologies associated with low dimensional Lie algebras
• Euler number and Betti numbers of homology groups of pre Lie superalgebra
• Deformed super brackets on forms of a manifold
• Structures Preserved by Consistently Graded Lie Superalgebras