{"paper":{"title":"Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"A. Borowiec, J. Lukierski, V.N. Tolstoy","submitted_at":"2015-11-11T20:56:22Z","abstract_excerpt":"We employ new calculational technique and present complete list of classical $r$-matrices for $D=4$ complex homogeneous orthogonal Lie algebra $\\mathfrak{o}(4;\\mathbb{C})$, the rotational symmetry of four-dimensional complex space-time. Further applying reality conditions we obtain the classical $r$-matrices for all possible real forms of $\\mathfrak{o}(4;\\mathbb{C})$: Euclidean $\\mathfrak{o}(4)$, Lorentz $\\mathfrak{o}(3,1)$, Kleinian $\\mathfrak{o}(2,2)$ and quaternionic $\\mathfrak{o}^{\\star}(4)$ Lie algebras. For $\\mathfrak{o}(3,1)$ we get known four classical $D=4$ Lorentz $r$-matrices, but f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03653","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"}