{"paper":{"title":"Basic quantizations of $D=4$ Euclidean, Lorentz, Kleinian and quaternionic $\\mathfrak{o}^{\\star}(4)$ symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"hep-th","authors_text":"A. Borowiec, J. Lukierski, V.N. Tolstoy","submitted_at":"2017-08-31T17:55:01Z","abstract_excerpt":"We construct firstly the complete list of five quantum deformations of $D=4$ complex homogeneous orthogonal Lie algebra $\\mathfrak{o}(4;\\mathbb{C})\\cong \\mathfrak{o}(3;\\mathbb{C})\\oplus \\mathfrak{o}(3;\\mathbb{C})$, describing quantum rotational symmetry of four-dimensional complex space-time, in particular we provide the corresponding universal quantum $R$-matrices. Further applying four possible reality conditions we obtain all sixteen Hopf-algebraic quantum deformations for the real forms of $\\mathfrak{o}(4;\\mathbb{C})$: Euclidean $\\mathfrak{o}(4)$, Lorentz $\\mathfrak{o}(3,1)$, Kleinian $\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.09848","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"}