{"paper":{"title":"$\\delta$-Novikov and $\\delta$-Novikov--Poisson algebras","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ivan Kaygorodov","submitted_at":"2025-05-12T20:20:29Z","abstract_excerpt":"This article considers the structure and properties of $\\delta$-Novikov algebras, a generalization of Novikov algebras characterized by a scalar parameter $\\delta$. It looks like $\\delta$-Novikov algebras have a richer structure than Novikov algebras. So, unlike Novikov algebras, they have non-commutative simple finite-dimensional algebras for $\\delta=-1.$ Additionally, we introduce $\\delta$-Novikov--Poisson algebras, extending several theorems from the classical Novikov--Poisson algebras. Specifically, we consider the commutator structure $[a, b] = a \\circ b - b \\circ a$ of $\\delta$-Novikov a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.08043","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/2505.08043/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"}