{"paper":{"title":"Adjacency preservers on invertible hermitian matrices II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Marko Orel","submitted_at":"2013-07-10T01:42:25Z","abstract_excerpt":"Maps that preserve adjacency on the set of all invertible hermitian matrices over a finite field are characterized. It is shown that such maps form a group that is generated by the maps $A\\mapsto PAP^{\\ast}$, $A\\mapsto A^{\\sigma}$, and $A\\mapsto A^{-1}$, where $P$ is an invertible matrix, $P^{\\ast}$ is its conjugate transpose, and $\\sigma$ is an automorphism of the underlying field. Bijectivity of maps is not an assumption but a conclusion. Moreover, adjacency is assumed to be preserved in one directions only.\n  The main result and author's previous result [16] are applied to characterize maps"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3484","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"}