{"paper":{"title":"Semigroups of I-type","license":"","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Michel Van den Bergh, Tatiana Gateva-Ivanova","submitted_at":"2003-08-08T11:12:47Z","abstract_excerpt":"Assume that $S$ is a semigroup generated by $\\{x_1,...,x_n\\}$, and let $\\Uscr$ be the multiplicative free commutative semigroup generated by $\\{u_1,...,u_n\\}$. We say that $S$ is of \\emph{$I$-typ}e if there is a bijection $v:\\Uscr\\r S$ such that for all $a\\in\\Uscr$, $\\{v(u_1a),... v(u_na)\\}=\\{x_1v(a),...,x_nv(a)\\}$. This condition appeared naturally in the work on Sklyanin algebras by John Tate and the second author. In this paper we show that the condition for a semigroup to be of $I$-type is related to various other mathematical notions found in the literature. In particular we show that sem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0308071","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0308071/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"}