{"paper":{"title":"Prime II$_1$ factors arising from irreducible lattices in products of rank one simple Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.FA"],"primary_cat":"math.OA","authors_text":"Adrian Ioana, Daniel Drimbe, Daniel Hoff","submitted_at":"2016-11-07T18:42:19Z","abstract_excerpt":"We prove that if $\\Gamma$ is an icc irreducible lattice in a product of connected non-compact rank one simple Lie groups with finite center, then the II$_1$ factor $L(\\Gamma)$ is prime. In particular, we deduce that the II$_1$ factors associated to the arithmetic groups $\\text{PSL}_2(\\mathbb Z[\\sqrt{d}])$ and $\\text{PSL}_2(\\mathbb Z[S^{-1}])$ are prime, for any square-free integer $d\\geq 2$ with $d\\not\\equiv 1 mod{4}$ and any finite non-empty set of primes $S$. This provides the first examples of prime II$_1$ factors arising from lattices in higher rank semisimple Lie groups. More generally, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.02209","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"}