{"paper":{"title":"An Invitation to Split Quaternionic Analysis","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.CV","authors_text":"Matvei Libine","submitted_at":"2010-09-13T23:54:46Z","abstract_excerpt":"Six years after William Rowan Hamilton's discovery of quaternions, in 1849 James Cockle introduced the algebra of split quaternions. (He called them ``coquaternions.'') In this paper we define regular functions on split quaternions and prove two different analogues of the Cauchy-Fueter formula for these functions.\n  In the paper \"Split quaternionic analysis and the separation of the series for SL(2,R) and SL(2,C)/SL(2,R)\" joint with Igor Frenkel we naturally apply the methods and formulas of quaternionic analysis to solve the problems of harmonic analysis on SL(2,R) and the imaginary Lobachevs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2540","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":""},"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"}