2022 The second Betti number of doubly weighted homology groups of a certain pre Lie superalgebra
Kentaro Mikami, Tadayoshi Mizutani
Tohoku Math. J. (2) 74(2): 301-311 (2022). DOI: 10.2748/tmj.20210208

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

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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

Information

Published: 2022
First available in Project Euclid: 6 July 2022

MathSciNet: MR4455870
zbMATH: 1521.17039
Digital Object Identifier: 10.2748/tmj.20210208

Subjects:
Primary: 53Dxx
Secondary: 17Bxx

Keywords: Betti number , homology groups , Lie superalgebras

Rights: Copyright © 2022 Tohoku University

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Vol.74 • No. 2 • 2022
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