{"paper":{"title":"Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras","license":"","headline":"","cross_cats":["hep-th","math.AG","math.QA","q-alg"],"primary_cat":"alg-geom","authors_text":"Viacheslav V. Nikulin","submitted_at":"1995-03-10T12:35:58Z","abstract_excerpt":"This is a continuation of our \"Lecture on Kac--Moody Lie algebras of the arithmetic type\" \\cite{25}.\n  We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\\times M \\to {\\Bbb Z}$ (i.e. hyperbolic lattice), reflection group $W\\subset W(S)$, fundamental polyhedron $\\Cal M$ of $W$ and an acceptable (corresponding to twisting coefficients) set $P({\\Cal M})\\subset M$ of vectors orthogonal to faces of $\\Cal M$ (simple roots). One can construct the corresponding Lorentzian Kac--Moody Lie algebra ${\\goth g}={\\goth g}^{\\prime\\prime}(A(S,W,P({\\Cal M})))$ which is graded b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9503003","kind":"arxiv","version":6},"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"}