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POTENTIALS OF A FROBENIUS-LIKE STRUCTURE

Published online by Cambridge University Press:  28 January 2018

CLAUS HERTLING
Affiliation:
Lehrstuhl für Mathematik VI, Universität Mannheim A5,6, 68131 Mannheim, Germany e-mail: hertling@math.uni-mannheim.de
ALEXANDER VARCHENKO
Affiliation:
Department of Mathematics, University of North Carolina at Chapel Hill Chapel Hill, NC 27599-3250, USA e-mail: anv@email.unc.edu
Corresponding

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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

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References

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