{"paper":{"title":"On a class of automorphisms in $\\mathbb{H}^2$ which resemble the property of preserving volume","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Fabio Vlacci, Jasna Prezelj","submitted_at":"2018-10-26T16:26:52Z","abstract_excerpt":"We give a possible extension for shears and overshears in the case of two non commutative (quaternionic) variables in relation with the associated vector fields and flows. We present a possible definition of volume preserving automorphisms, even though there is no quaternionic volume form on $\\mathbb{H}^2$ . Using this, we determine a class of quaternionic automorphisms for which the Ander- sen-Lempert theory applies. Finally, we exhibit an example of a quaternionic automor- phism, which is not in the in the closure of the set of finite compositions of volume preserving quaternionic shears."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11412","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"}