{"paper":{"title":"Singular Degenerations of Lie Supergroups of Type $D(2,1;a)$","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RA","authors_text":"Fabio Gavarini, Kenji Iohara","submitted_at":"2017-09-14T11:49:00Z","abstract_excerpt":"The complex Lie superalgebras $\\mathfrak{g}$ of type $D(2,1;a)$ - also denoted by $\\mathfrak{osp}(4,2;a) $ - are usually considered for \"non-singular\" values of the parameter $a$, for which they are simple. In this paper we introduce five suitable integral forms of $\\mathfrak{g}$, that are well-defined at singular values too, giving rise to \"singular specializations\" that are no longer simple: this extends the family of simple objects of type $D(2,1;a)$ in five different ways. The resulting five families coincide for general values of $a$, but are different at \"singular\" ones: here they provid"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04717","kind":"arxiv","version":4},"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"}