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arXiv · 1804.07073

Darboux coordinates for Hamiltonian structures defined by Novikov algebras

Ian A. B. Strachan
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Abstract

The Gauss-Manin equations are solved for a class of flat-metrics defined by Novikov algebras, this generalizing a result of Balinskii and Novikov who solved this problem in the case of commutative Novikov algebras (where the algebraic conditions reduce to those of a Frobenius algebra). The problem stems from the theory of first-order Hamiltonian operators and their reduction to a constant, or Darboux, form. The monodromy group associated with the Novikov algebra gives rise to an orbit space, which is, for a wide range of Novikov algebras, a cyclic quotient singularity.

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Ian A. B. Strachan. 2018-04-19. Darboux coordinates for Hamiltonian structures defined by Novikov algebras. https://arxiv.org/abs/1804.07073

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