{"paper":{"title":"The proof of the Kontsevich periodicity conjecture on noncommutative birational transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP","math.QA","math.RT"],"primary_cat":"math.RA","authors_text":"Natalia Iyudu, Stanislav Shkarin","submitted_at":"2013-05-08T21:59:47Z","abstract_excerpt":"For an arbitrary associative unital ring $R$, let $J_1$ and $J_2$ be the following noncommutative birational partly defined involutions on the set $M_3(R)$ of $3\\times 3$ matrices over $R$: $J_1(M)=M^{-1}$ (the usual matrix inverse) and $J_2(M)_{jk}=(M_{kj})^{-1}\\,$ (the transpose of the Hadamard inverse).\n  We prove the following surprising conjecture by Kontsevich saying that $(J_2\\circ J_1)^3$ is the identity map modulo the ${\\rm Diag}_{L} \\times \\rm{Diag}_R$ action $(D_1,D_2)(M)=D_1^{-1}MD_2$ of pairs of invertible diagonal matrices.\n  That is, we show that for each $M$ in the domain where"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.1965","kind":"arxiv","version":3},"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"}