{"paper":{"title":"Braidings on the category of bimodules, Azumaya algebras and epimorphisms of rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.QA","authors_text":"A.L. Agore, G. Militaru, S. Caenepeel","submitted_at":"2011-08-12T07:03:41Z","abstract_excerpt":"Let $A$ be an algebra over a commutative ring $k$. We prove that braidings on the category of $A$-bimodules are in bijective correspondence to canonical R-matrices, these are elements in $A\\ot A\\ot A$ satisfying certain axioms. We show that all braidings are symmetries. If $A$ is commutative, then there exists a braiding on ${}_A\\Mm_A$ if and only if $k\\to A$ is an epimorphism in the category of rings, and then the corresponding $R$-matrix is trivial. If the invariants functor $G = (-)^A:\\{}_A\\Mm_A\\to \\Mm_k$ is separable, then $A$ admits a canonical R-matrix; in particular, any Azumaya algebra"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.2575","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"}