{"paper":{"title":"Approximation properties for $p$-adic symplectic groups and lattices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Benben Liao","submitted_at":"2015-09-16T05:48:03Z","abstract_excerpt":"Let $G$ be the symplectic group $Sp_4$ over a non Archimedean local field of any characteristic. It is proved in this paper that for $p\\in[1,4/3)\\cup (4,\\infty]$ neither the group $G$ nor its lattices have the property of approximation by Schur multipliers on Schatten $p$ class ($AP_{pcb}^{Schur}$) of Lafforgue and de la Salle. As a consequence, for any lattice $\\Gamma$ in $G,$ the associated non-commutative $L^p$ space $L^p(L\\Gamma)$ of its von Neumann algebra $L(\\Gamma)$ fails the operator space approximation property (OAP) and completely bounded approximation property (CBAP) for $p\\in[1,4/3"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.04814","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"}