{"paper":{"title":"Extremality of Quaternionic J{\\o}rgensen Inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.CV","authors_text":"Abhishek Mukherjee, Krishnendu Gongopadhyay","submitted_at":"2015-03-30T19:14:30Z","abstract_excerpt":"Let ${\\rm SL(2, \\mathbb H)}$ be the group of $2 \\times 2$ quaternionic matrices with Dieudonn\\'e determinant $1$. The group ${\\rm SL(2, \\mathbb H)}$ acts on the five dimensional hyperbolic space by isometries. We investigate extremality of J\\o{}rgensen type inequalities in ${\\rm SL(2, \\mathbb H)}$. Along the way, we derive J\\o{}rgensen type inequalities for quaternionic M\\\"obius transformations which extend earlier inequalities obtained by Waterman and Kellerhals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.08802","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":""},"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"}