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arXiv · 1712.08389

Potentials of a Frobenius like structure

Claus Hertling·Alexander Varchenko
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Abstract

This paper proves the existence of potentials of the first and second kind of a Frobenius like structure in a frame which encompasses families of arrangements. The frame uses the notion of matroids. For the proof of the existence of the potentials, a power series ansatz is made. The proof that it works requires that certain decompositions of tuples of coordinate vector fields are related by certain elementary transformations. This is shown with a nontrivial result on matroid partition.

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Claus Hertling, Alexander Varchenko. 2017-12-22. Potentials of a Frobenius like structure. https://arxiv.org/abs/1712.08389

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