{"paper":{"title":"Transposed Poisson structures on Schrodinger algebra in (n+1)-dimensional space-time","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Abror Khudoyberdiyev, Xiaomin Tang, Yang Yang","submitted_at":"2023-03-02T12:29:30Z","abstract_excerpt":"Transposed Poisson structures on the Schr\\\"{o}dinger algebra in $(n+1)$-dimensional space-time of Schr\\\"{o}dinger Lie groups are described. It was proven that the Schr\\\"{o}dinger algebra $\\mathcal{S}_{n}$ in case of $n\\neq 2$ does not have non-trivial $\\frac{1}{2}$-derivations and as it follows it does not admit non-trivial transposed Poisson structures. All $\\frac{1}{2}$-derivations and transposed Poisson structures for the algebra $\\mathcal{S}_{2}$ are obtained. Also, we proved that the Schr\\\"{o}dinger algebra $\\mathcal{S}_{2}$ admits a non-trivial ${\\rm Hom}$-Lie structure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.08180","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.08180/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"}