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Classification of 1+0 two-dimensional Hamiltonian operators

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arxiv 2410.22455 v2 pith:UYVR6WHO submitted 2024-10-29 math-ph math.MPnlin.SI

Alessandra Rizzo This is my paper · ORCID
classification math-phmath.MPnlin.SI
keywords operatorsclassificationdegeneratehamiltoniananalyzingcasescoefficientscomplete
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In this paper, we study Hamiltonian operators which are sum of a first order operator and of a Poisson tensor, in two spatial independent variables. In particular, a complete classification of these operators is presented in two and three components, analyzing both the cases of degenerate and non degenerate leading coefficients.

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  1. Lie algebras with compatible scalar products for non-homogeneous Hamiltonian operators

    math-ph 2025-02 conditional novelty 5.0 of 10

    Non-homogeneous 1+0 Hamiltonian operators in Darboux form are characterized by a Lie algebra, a non-degenerate quadratic Casimir, and a 2-cocycle, with an explicit catalogue of all cases through dimension 6.

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