{"paper":{"title":"Transposed Poisson structures on Lie incidence algebras","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ivan Kaygorodov, Mykola Khrypchenko","submitted_at":"2023-09-01T08:36:17Z","abstract_excerpt":"Let $X$ be a finite connected poset, $K$ a field of characteristic zero and $I(X,K)$ the incidence algebra of $X$ over $K$ seen as a Lie algebra under the commutator product. In the first part of the paper we show that any $\\frac{1}{2}$-derivation of $I(X,K)$ decomposes into the sum of a central-valued $\\frac 12$-derivation, an inner $\\frac{1}{2}$-derivation and a $\\frac{1}{2}$-derivation associated with a map $\\sigma:X^2_<\\to K$ that is constant on chains and cycles in $X$. In the second part of the paper we use this result to prove that any transposed Poisson structure on $I(X,K)$ is the sum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.00332","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/2309.00332/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"}