Abstract
The Schouten-Nijenhuis bracket ([4],[5]) is used to describe whether a 2-vector field becomes a Poisson tensor field or not, due to Lichnerowicz, and it is a very popular and useful tool in Poisson geometry. In this note we observe that the bracket has a very natural and simple notion in its root, namely, skew-symmetry and the Leibniz’ rule. We then give an easy proof for the super Jacobi identity of the Schouten-Nijenhuis bracket.
Partially supported by Grant-in-Aid for Scientific Research (C) (No. 10640057), The Ministry of Education, Science, Sport and Culture, Japan.
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Mikami, K. (2001). An Interpretation of the Schouten-Nijenhuis Bracket. In: Maeda, Y., Moriyoshi, H., Omori, H., Sternheimer, D., Tate, T., Watamura, S. (eds) Noncommutative Differential Geometry and Its Applications to Physics. Mathematical Physics Studies, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0704-7_8
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DOI: https://doi.org/10.1007/978-94-010-0704-7_8
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