{"paper":{"title":"Modular lattices from finite projective planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Tathagata Basak","submitted_at":"2012-10-08T22:04:25Z","abstract_excerpt":"Using the geometry of the projective plane over the finite field F_q, we construct a Hermitian Lorentzian lattice L_q of dimension (q^2 + q + 2) defined over a certain number ring $\\cO$ that depends on q. We show that infinitely many of these lattices are p-modular, that is, p L'_q = L_q, where p is some prime in $\\cO$ such that |p|^2 = q. The reflection group of the Lorentzian lattice obtained for q = 3 seems to be closely related to the monster simple group via the presentation of the bimonster as a quotient of the Coxeter group on the incidence graph of P^2(F_3). The Lorentzian lattices L_q"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.2431","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"}