{"paper":{"title":"Ideal structure of crossed products by endomorphisms via reversible extensions of $C^*$-dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"B. K. Kwasniewski","submitted_at":"2014-04-19T06:53:25Z","abstract_excerpt":"We consider an extendible endomorphism $\\alpha$ of a $C^*$-algebra $A$. We associate to it a canonical $C^*$-dynamical system $(B,\\beta)$ that extends $(A,\\alpha)$ and is `reversible' in the sense that the endomorphism $\\beta$ admits a unique regular transfer operator $\\beta_*$. The theory for $(B,\\beta)$ is analogous to the theory of classic crossed products by automorphisms, and the key idea is to describe the counterparts of classic notions for $(B,\\beta)$ in terms of the initial system $(A,\\alpha)$.\n  We apply this idea to study the ideal structure of a non-unital version of the crossed pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4928","kind":"arxiv","version":2},"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"}