{"paper":{"title":"Computing cohomology spaces of left-invariant involutive structures on $\\mathrm{SU}(2)$: examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Gabriel Ara\\'ujo","submitted_at":"2019-08-25T19:55:37Z","abstract_excerpt":"In these notes we study left-invariant involutive structures on $\\mathrm{SU}(2)$, the most na\\\"ive non-commutative compact Lie group. We determine closedness of the range (in the smooth topology) of a single complex vector field spanning the standard CR structure of $\\mathrm{SU}(2)$ and also compute the smooth cohomology spaces of a corank $1$ structure. In our approach, it is fundamental to understand concretely the irreducible representations of the ambient Lie group and how left-invariant vector fields operate on their matrix coefficients (which we borrow from the book of Ruzhansky and Turu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.10207","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/1908.10207/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"}