{"paper":{"title":"$K$-theory of Leavitt path algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.KT","authors_text":"Guillermo Corti\\~nas, Miquel Brustenga, Pere Ara","submitted_at":"2009-02-28T09:25:42Z","abstract_excerpt":"Let $E$ be a row-finite quiver and let $E_0$ be the set of vertices of $E$; consider the adjacency matrix $N'_E=(n_{ij})\\in\\Z^{(E_0\\times E_0)}$, $n_{ij}=#\\{$ arrows from $i$ to $j\\}$. Write $N^t_E$ and 1 for the matrices $\\in \\Z^{(E_0\\times E_0\\setminus\\Sink(E))}$ which result from $N'^t_E$ and from the identity matrix after removing the columns corresponding to sinks. We consider the $K$-theory of the Leavitt algebra $L_R(E)=L_\\Z(E)\\otimes R$. We show that if $R$ is either a Noetherian regular ring or a stable $C^*$-algebra, then there is an exact sequence ($n\\in\\Z$) \\[ K_n(R)^{(E_0\\setminus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.0056","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"}