{"paper":{"title":"Fractal nil graded Lie, associative, Poisson, and Jordan superalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Ivan Shestakov, Victor Petrogradsky","submitted_at":"2018-04-20T03:22:02Z","abstract_excerpt":"We construct a just infinite fractal 3-generated Lie superalgebra $\\mathbf Q$ over arbitrary field, which gives rise to an associative hull $\\mathbf A$, a Poisson superalgebra $\\mathbf P$, and two Jordan superalgebras $\\mathbf J$, $\\mathbf K$. One has a natural filtration for $\\mathbf A$ which associated graded algebra has a structure of a Poisson superalgebra and $\\mathrm{gr} \\mathbf A\\cong\\mathbf P$, also $\\mathbf P$ admits an algebraic quantization. The Lie superalgebra $\\mathbf Q$ is finely $\\mathbb Z^3$-graded by multidegree in the generators, $\\mathbf A$, $\\mathbf P$ are $\\mathbb Z^3$-gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.08441","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"}