FERAPONTOV, E.V., PAVLOV, M.V. and VITOLO, R.F., 2016. Towards the classification of homogeneous third-order Hamiltonian operators. International Mathematics Research Notices, In Press
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.
This paper is in closed access untill Jan 5th 2017.
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