{"paper":{"title":"On the Identity Problem for the Special Linear Group and the Heisenberg Group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Igor Potapov, Reino Niskanen, Sang-Ki Ko","submitted_at":"2017-06-13T17:10:37Z","abstract_excerpt":"We study the identity problem for matrices, i.e., whether the identity matrix is in a semigroup generated by a given set of generators. In particular we consider the identity problem for the special linear group following recent NP-completeness result for ${\\rm SL}(2,\\mathbb{Z})$ and the undecidability for ${\\rm SL}(4,\\mathbb{Z})$ generated by $48$ matrices. First we show that there is no embedding from pairs of words into $3\\times3$ integer matrices with determinant one, i.e., into ${\\rm SL}(3,\\mathbb{Z})$ extending previously known result that there is no embedding into $\\mathbb{C}^{2\\times "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.04166","kind":"arxiv","version":5},"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"}