{"paper":{"title":"Two relations that generalize the $q$-Serre relations and the Dolan-Grady relations","license":"","headline":"","cross_cats":["math-ph","math.CO","math.MP","math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Paul Terwilliger","submitted_at":"2003-07-01T22:18:25Z","abstract_excerpt":"We define an algebra on two generators which we call the Tridiagonal algebra, and we consider its irreducible modules. The algebra is defined as follows. Let K denote a field, and let $\\beta, \\gamma, \\gamma^*, \\varrho, \\varrho^*$ denote a sequence of scalars taken from K. The corresponding Tridiagonal algebra $T$ is the associative K-algebra with 1 generated by two symbols $A$, $A^*$ subject to the relations (i) \\lbrack A,A^2A^*-\\beta AA^*A + A^*A^2 -\\gamma (AA^*+A^*A)- \\varrho A^*\\rbrack = 0,\n  (ii) \\lbrack A^*,A^{*2}A-\\beta A^*AA^* + AA^{*2} -\\gamma^* (A^*A+AA^*)- \\varrho^* A\\rbrack = 0, whe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0307016","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/0307016/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"}