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 $S^2(Lambda^2V)$ that lie in the kernel of the natural map $S^2(Lambda^2V) o Lambda^4V$. 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 $nleq 4$.

Towards the classification of homogeneous third-order Hamiltonian operators

VITOLO, Raffaele
2016-01-01

Abstract

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 $S^2(Lambda^2V)$ that lie in the kernel of the natural map $S^2(Lambda^2V) o Lambda^4V$. 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 $nleq 4$.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/402471
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