Darboux coordinates for Hamiltonian structures defined by Novikov algebras
Exactly Solvable and Integrable Systems
2021-05-24 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.1804.07073,
title = {Darboux coordinates for Hamiltonian structures defined by Novikov algebras},
author = {Ian A. B. Strachan},
journal= {arXiv preprint arXiv:1804.07073},
year = {2021}
}