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Towards the classification of homogeneous third-order Hamiltonian operators

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journal contribution
posted on 04.02.2016 by Evgeny Ferapontov, Maxim V. Pavlov, R.F. Vitolo
Let V be a vector space of dimension n + 1. We demonstrate that n-component third-order Hamiltonian operators of differential-geometric type are parametrised by the algebraic variety of elements of rank n in S2(Λ2V) that lie in the kernel of the natural map S2(Λ2V)→Λ4V. Non-equivalent operators correspond to different orbits of the natural action of SL(n + 1). Based on this result, we obtain a classification of such operators for n≤4.

Funding

This paper was supportted by GNFM of the Istituto Nazionale di Alta Matematica, the Istituto Nazionale di Fisica Nucleare, and the Dipartimento di Matematica e Fisica \E. De Giorgi" of the Universita del Salento. MVP's work was also partially supported by the grant of Presidium of RAS \Fundamental Problems of Nonlinear Dynamics" and by the RFBR grant 11-01-0019

History

School

  • Science

Department

  • Mathematical Sciences

Published in

International Mathematics Research Notices

Pages

? - ? (27)

Citation

FERAPONTOV, E.V., PAVLOV, M.V. and VITOLO, R.F., 2016. Towards the classification of homogeneous third-order Hamiltonian operators. International Mathematics Research Notices, 2016 (22), pp. 6829-6855.

Publisher

© The Authors. Published by Oxford University Press

Version

AM (Accepted Manuscript)

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This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2016

Notes

This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record is available online at http://dx.doi.org/10.1093/imrn/rnv369.

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en

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