{"paper":{"title":"PreHamiltonian and Hamiltonian operators for differential-difference equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alexander V. Mikhailov, Jing Ping Wang, Sylvain Carpentier","submitted_at":"2018-08-08T22:35:21Z","abstract_excerpt":"In this paper we are developing a theory of rational (pseudo) difference Hamiltonian operators, focusing in particular on its algebraic aspects. We show that a pseudo--difference Hamiltonian operator can be represented as a ratio $AB^{-1}$ of two difference operators with coefficients from a difference field $\\mathcal{F}$ where $A$ is preHamiltonian. A difference operator $A$ is called preHamiltonian if its image is a Lie subalgebra with respect to the Lie bracket of evolutionary vector fields on $\\mathcal{F}$. We show that a skew-symmetric difference operator is Hamiltonian if and only if it "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02957","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}