{"paper":{"title":"The Euclidean Hopf algebra $U_q(e^N)$ and its fundamental Hilbert space representations","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"hep-th","authors_text":"Gaetano Fiore","submitted_at":"1994-07-29T15:59:29Z","abstract_excerpt":"We construct the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\\rn_q^N\\lcross SO_{q^{-1}}(N))$ by realizing it as a subalgebra of the differential algebra $\\DFR$ on the quantum Euclidean space $\\rn_q^N$; in fact, we extend our previous realization \\cite{fio4} of $U_{q^{-1}}(so(N))$ within $\\DFR$ through the introduction of q-derivatives as generators of q-translations. The fundamental Hilbert space representations of $U_q(e^N)$ turn out to be of highest weight type and rather simple `` lattice-regularized '' versions of the classical ones. The vectors of a basis of the singlet (i.e. zero-spin"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9407195","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"}