{"paper":{"title":"Classification of $N$-(super)-extended Poincar\\'e algebras and bilinear invariants of the spinor representation of $Spin(p,q)$","license":"","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Dmitry V. Alekseevsky, Vicente Cort\\'es","submitted_at":"1995-11-28T00:00:00Z","abstract_excerpt":"We classify extended Poincar\\'e Lie super algebras and Lie algebras of any signature (p,q), that is Lie super algebras and Z_2-graded Lie algebras g = g_0 + g_1, where g_0 = so(V) + V is the (generalized) Poincar\\'e Lie algebra of the pseudo Euclidean vector space V = R^{p,q} of signature (p,q) and g_1 = S is the spinor so(V)-module extended to a g_0-module with kernel V. The remaining super commutators {g_1,g_1} (respectively, commutators [g_1, g_1]) are defined by an so(V)-equivariant linear mapping vee^2 g_1 -> V (respectively,  wedge^2 g_1 -> V). Denote by P^+(n,s) (respectively, P^-(n,s))"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9511215","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"}