{"paper":{"title":"Solomon-Terao algebra of hyperplane arrangements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG","math.CV"],"primary_cat":"math.AC","authors_text":"Satoshi Murai, Takuro Abe, Toshiaki Maeno, Yasuhide Numata","submitted_at":"2018-02-12T14:18:34Z","abstract_excerpt":"We introduce a new algebra associated with a hyperplane arrangement $\\mathcal{A}$, called the Solomon-Terao algebra $\\mbox{ST}(\\mathcal{A},\\eta)$, where $\\eta$ is a homogeneous polynomial. It is shown by Solomon and Terao that $\\mbox{ST}(\\mathcal{A},\\eta)$ is Artinian when $\\eta$ is generic. This algebra can be considered as a generalization of coinvariant algebras in the setting of hyperplane arrangements. The class of Solomon-Terao algebras contains cohomology rings of regular nilpotent Hessenberg varieties. We show that $\\mbox{ST}(\\mathcal{A},\\eta)$ is a complete intersection if and only if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04056","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"}