{"paper":{"title":"Supertropical $\\operatorname{SL}_n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT","math.RT"],"primary_cat":"math.RA","authors_text":"Adi Niv, Louis Rowen, Zur Izhakian","submitted_at":"2015-08-18T23:22:57Z","abstract_excerpt":"Extending earlier work on supertropical adjoints and applying symmetrization, we provide a symmetric supertropical version $\\operatorname {SLS}_n$ of the special linear group, which we partition into submonoids, based on \"quasi-identity\" matrices, and we display maximal sub-semigroups of $\\operatorname {SLS}_n$. We also study the monoid generated by $\\operatorname {SLS}_n$. Several illustrative examples are given of unexpected behavior. We describe the action of elementary matrices on $\\operatorname {SLS}_n$, which enables one to connect different matrices in $\\operatorname {SLS}_n$, but in a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04483","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"}