{"paper":{"title":"A spanning set and potential basis of the mixed Hecke algebra on two fixed strands","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dimitrios Kodokostas, Sofia Lambropoulou","submitted_at":"2017-04-12T09:48:09Z","abstract_excerpt":"The mixed braid groups $B_{2,n}, \\ n \\in \\mathbb{N}$, with two fixed strands and $n$ moving ones, are known to be related to the knot theory of certain families of $3$-manifolds. In this paper we define the mixed Hecke algebra $\\mathrm{H}_{2,n}(q)$ as the quotient of the group algebra ${\\mathbb Z}\\, [q^{\\pm 1}] \\, B_{2,n}$ over the quadratic relations of the classical Iwahori-Hecke algebra for the braiding generators. We furhter provide a potential basis $\\Lambda_n$ for $\\mathrm{H}_{2,n}(q)$, which we prove is a spanning set for the $\\mathbb{Z}[q^{\\pm 1}]$-additive structure of this algebra. T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03676","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"}