{"paper":{"title":"On the Hodge-type decomposition and cohomolgy groups of $k$-Cauchy-Fueter complexes over domains in the quaternionic space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CV","authors_text":"Der-Chen Chang, Irina Markina, Wei Wang","submitted_at":"2015-08-12T11:10:26Z","abstract_excerpt":"The $k$-Cauchy-Fueter operator $ D_0^{(k) } $ on one dimensional quaternionic space $\\mathbb{H}$ is the Euclidean version of helicity $\\frac k 2$ massless field operator on the Minkowski space in physics. The $k$-Cauchy-Fueter equation for $k\\geq 2$ is overdetermined and its compatibility condition is given by the $k$-Cauchy-Fueter complex. In quaternionic analysis, these complexes play the role of Dolbeault complex in several complex variables. We prove that a natural boundary value problem associated to this complex is regular. Then by using the theory of regular boundary value problems, we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02875","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"}