{"paper":{"title":"Crossed products and twisted $k$-graph algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Alex Kumjian, David Pask, Nathan Brownlowe, Valentin Deaconu","submitted_at":"2014-07-24T02:20:21Z","abstract_excerpt":"An automorphism $\\beta$ of a $k$-graph $\\Lambda$ induces a crossed product $C^* ( \\Lambda ) \\rtimes_\\beta \\mathbb{Z}$ which is isomorphic to a $(k+1)$-graph algebra $C^* ( \\Lambda \\times_\\beta \\mathbb{Z})$. In this paper we show how this process interacts with $k$-graph $C^*$-algebras which have been twisted by an element of their second cohomology group. This analysis is done using a long exact sequence in cohomology associated to this data. We conclude with some examples"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6427","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"}