{"paper":{"title":"The q-Euclidean algebra $U_q(e^N)$ and the corresponding q-Euclidean lattice","license":"","headline":"","cross_cats":["hep-th","math.QA"],"primary_cat":"q-alg","authors_text":"Gaetano Fiore","submitted_at":"1995-07-01T22:56:09Z","abstract_excerpt":"We review the Euclidean Hopf algebra $U_q(e^N)$ dual of $Fun(\\rn_q^N\\lcross SO_{q^{-1}}(N))$ and describe its fundamental Hilbert space representations \\cite{fioeu}, which turn out to be rather simple \"lattice-regularized\" versions of the classical ones, in the sense that the spectra of squared momentum components are discrete and the corresponding eigenfunctions normalizable.These representations can be regarded as describing a quantum system consisting of one free particle on the quantum Euclidean space. A suitable notion of classical limit is introduced, so that we recover the classical con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9506028","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"}