{"paper":{"title":"A new family of Poisson algebras and their deformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.RA","authors_text":"Cesar Lecoutre, Susan J. Sierra","submitted_at":"2016-11-14T09:51:44Z","abstract_excerpt":"Let $\\Bbbk$ be a field of characteristic zero. For any positive integer $n$ and any scalar $a\\in\\Bbbk$, we construct a family of Artin-Schelter regular algebras $R(n,a)$, which are quantisations of Poisson structures on $\\Bbbk[x_0,\\dots,x_n]$. This generalises an example given by Pym when $n=3$. For a particular choice of the parameter $a$ we obtain new examples of Calabi-Yau algebras when $n\\geq 4$. We also study the ring theoretic properties of the algebras $R(n,a)$. We show that the point modules of $R(n,a)$ are parameterised by a bouquet of rational normal curves in $\\mathbb{P}^{n}$, and t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.04306","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":""},"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"}