{"paper":{"title":"Classification and structure of generalized Legendrian racks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.QA"],"primary_cat":"math.GT","authors_text":"Luc Ta","submitted_at":"2025-04-17T06:05:09Z","abstract_excerpt":"We study algebraic aspects of generalized Legendrian racks, which are nonassociative structures based on the Legendrian Reidemeister moves.\n  We answer an open question characterizing the group of GL-structures on a given rack. As applications, we classify several infinite families of GL-racks. We also compute automorphism groups of dihedral GL-quandles.\n  Then we compute the centers of the category of GL-racks and several of its full subcategories. We also construct an equivalence of categories between racks and GL-quandles.\n  We also study tensor products of racks and GL-racks coming from un"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.12671","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.12671/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}