{"paper":{"title":"Exel-Pardo algebras with a twist","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.QA","math.RA","math.RT"],"primary_cat":"math.OA","authors_text":"Guillermo Corti\\~nas","submitted_at":"2023-09-25T17:52:31Z","abstract_excerpt":"Katsura associated a $C^*$-algebra $C^*_{A,B}$ to integral matrices $A\\ge 0$ and $B$ of the same size, gave sufficient conditions on $(A,B)$ making it simple purely infinite (SPI), and proved that any separable $C^*$-algebra $KK$-isomorphic to a cone of an element $\\xi\\in KK(C(S^1)^n,C(S^1)^n)$ in Kasparov's $KK$ is $KK$-isomorphic to an SPI $C^*_{A,B}$. Here we introduce, for the data of a commutative ring $\\ell$, matrices $A,B$ as above and $C$ of the same size with coefficients in the group $\\mathcal{U}(\\ell)$ of invertible elements, an $\\ell$-algebra $\\mathcal{O}_{A,B}^C$, the twisted Kats"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.14325","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.14325/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"}