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arXiv · 2504.15010

The Schouten-Nijenhuis bracket in infinite dimensions

Peter W. Michor
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Abstract

The Schouten-Nijenhuis bracket on smooth infinite-dimensional manifolds $M$ is developed in two steps: For summable multivector fields whose pointwise dual are all differential form, and in an extended form for multivector fields which are sections of $L^{\bullet}_{\text{skew}}(T^*M,\mathbb R)$. We need to either assume that $C^{\infty}(M)$ separates points on $TM$, or consider sheaves of local sections.

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Peter W. Michor. 2025-04-21. The Schouten-Nijenhuis bracket in infinite dimensions. https://arxiv.org/abs/2504.15010

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