{"paper":{"title":"Semidirect Product of Groupoids, Its Representations and Random Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Leszek Pysiak, Michael Heller, Micha{\\l} Eckstein, Wies{\\l}aw Sasin","submitted_at":"2011-07-09T12:08:42Z","abstract_excerpt":"One of pressing problems in mathematical physics is to find a generalized Poincar\\'e symmetry that could be applied to nonflat space-times. As a step in this direction we define the semidirect product of groupoids $\\Gamma_0 \\rtimes \\Gamma_1$ and investigate its properties. We also define the crossed product of a bundle of algebras with the groupoid $\\Gamma_1$ and prove that it is isomorphic to the convolutive algebra of the groupoid $\\Gamma_0 \\rtimes \\Gamma_1$. We show that families of unitary representations of semidirect product groupoids in a bundle of Hilbert spaces are random operators. A"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.1775","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"}