Abstract
The space of multi-vector fields on a manifold has a structure of ${\mathbb{Z}}$-graded Lie superalgebras under the Schouten bracket. (We call such an algebra a pre Lie superalgebra.) As in the case of Lie algebras, we have the associated homology groups similarly. We treat the case where the underlying manifold is a Euclidean $n$-space, and the coefficients are polynomials. Under such conditions, we show the vanishing of the second homology group of the chain complexes which are doubly indexed by the pairs of integers $(w,h)$, which we call weights. We specially treat the case $w=h$ in this article.
Citation
Kentaro Mikami. Tadayoshi Mizutani. "The second Betti number of doubly weighted homology groups of a certain pre Lie superalgebra." Tohoku Math. J. (2) 74 (2) 301 - 311, 2022. https://doi.org/10.2748/tmj.20210208
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