{"paper":{"title":"Quantizations of D=3 Lorentz symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"J. Lukierski, V.N. Tolstoy","submitted_at":"2016-12-12T19:42:46Z","abstract_excerpt":"Using the isomorphism $\\mathfrak{o}(3;\\mathbb{C})\\simeq\\mathfrak{sl}(2;\\mathbb{C})$ we develop a new simple algebraic technique for complete classification of quantum deformations (the classical $r$-matrices) for real forms $\\mathfrak{o}(3)$ and $\\mathfrak{o}(2,1)$ of the complex Lie algebra $\\mathfrak{o}(3;\\mathbb{C})$ in terms of real forms of $\\mathfrak{sl}(2;\\mathbb{C})$: $\\mathfrak{su}(2)$, $\\mathfrak{su}(1,1)$ and $\\mathfrak{sl}(2;\\mathbb{R})$. We prove that the $D=3$ Lorentz symmetry $\\mathfrak{o}(2,1)\\simeq\\mathfrak{su}(1,1)\\simeq\\mathfrak{sl}(2;\\mathbb{R})$ has three different Hopf-al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.03866","kind":"arxiv","version":2},"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"}