{"paper":{"title":"The Z_2 x Z_2-graded Lie superalgebra pso(2m+1|2n) and new parastatistics representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.RT","quant-ph"],"primary_cat":"math-ph","authors_text":"J. Van der Jeugt, N.I. Stoilova","submitted_at":"2017-11-06T19:42:09Z","abstract_excerpt":"When the relative commutation relations between a set of m parafermions and n parabosons are of ``relative parafermion type'', the underlying algebraic structure is the classical orthosymplectic Lie superalgebra osp(2m+1|2n). The relative commutation relations can also be chosen differently, of ``relative paraboson type''. In this second case, the underlying algebraic structure is no longer an ordinary Lie superalgebra, but a Z_2 x Z_2$-graded Lie superalgebra, denoted here by pso(2m+1|2n). The identification of this new algebraic structure was performed by Tolstoy, amongst others. In the pres"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02136","kind":"arxiv","version":1},"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"}