{"paper":{"title":"Spin Calogero models obtained from dynamical r-matrices and geodesic motion","license":"","headline":"","cross_cats":["hep-th","math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"B.G. Pusztai, L. Feher","submitted_at":"2005-07-25T09:15:53Z","abstract_excerpt":"We study classical integrable systems based on the Alekseev-Meinrenken dynamical r-matrices corresponding to automorphisms of self-dual Lie algebras, ${\\cal G}$. We prove that these r-matrices are uniquely characterized by a non-degeneracy property and apply a construction due to Li and Xu to associate spin Calogero type models with them. The equation of motion of any model of this type is found to be a projection of the natural geodesic equation on a Lie group $G$ with Lie algebra ${\\cal G}$, and its phase space is interpreted as a Hamiltonian reduction of an open submanifold of the cotangent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0507062","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0507062/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}