{"paper":{"title":"On the hermiticity of q-differential operators and forms on the quantum Euclidean spaces R_q^N","license":"","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Gaetano Fiore","submitted_at":"2004-03-26T15:00:23Z","abstract_excerpt":"We show that the complicated *-structure characterizing for positive q the U_qso(N)-covariant differential calculus on the non-commutative manifold R_q^N boils down to similarity transformations involving the ribbon element of a central extension of U_qso(N) and its formal square root v. Subspaces of the spaces of functions and of p-forms on R_q^N are made into Hilbert spaces by introducing non-conventional ``weights'' in the integrals defining the corresponding scalar products, namely suitable positive-definite q-pseudodifferential operators realizing the action of v^{\\pm 1}; this serves to m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0403463","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"}