{"paper":{"title":"Certain families of Polynomials arising in the study of hyperelliptic Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Ben Cox, Kaiming Zhao","submitted_at":"2016-02-03T19:54:37Z","abstract_excerpt":"The associative ring $R(P(t))=\\mathbb C[t^{\\pm1},u \\,|\\, u^2=P(t)]$, where $P(t)=\\sum_{i=0}^na_it^i=\\prod_{k=1}^n(t-\\alpha_i)$ with $\\alpha_i\\in\\mathbb C$ pairwise distinct, is the coordinate ring of a hyperelliptic curve. The Lie algebra $\\mathcal{R}(P(t))=\\text{Der}(R(P(t)))$ of derivations is called the hyperelliptic Lie algebra associated to $P(t)$.\n  In this paper we describe the universal central extension of $\\text{Der}(R(P(t)))$ in terms of certain families of polynomials which in a particular case are associated Legendre polynomials. Moreover we describe certain families of polynomial"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.01432","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"}