{"paper":{"title":"Homotopy invariance through small stabilizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RA"],"primary_cat":"math.KT","authors_text":"Beatriz Abadie, Guillermo Corti\\~nas","submitted_at":"2012-12-24T12:19:48Z","abstract_excerpt":"We associate an algebra $\\Gami(\\fA)$ to each bornological algebra $\\fA$. The algebra $\\Gami(\\fA)$ contains a two-sided ideal $I_{S(\\fA)}$ for each symmetric ideal $S\\triqui\\elli$ of bounded sequences of complex numbers. In the case of $\\Gami=\\Gami(\\C)$, these are all the two-sided ideals, and $I_S\\mapsto J_S=\\cB I_S\\cB$ gives a bijection between the two-sided ideals of $\\Gami$ and those of $\\cB=\\cB(\\ell^2)$. We prove that Weibel's $K$-theory groups $KH_*(I_{S(\\fA)})$ are homotopy invariant for certain ideals $S$ including $c_0$ and $\\ell^p$. Moreover, if either $S=c_0$ and $\\fA$ is a local $C^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.5901","kind":"arxiv","version":3},"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"}