{"paper":{"title":"The Weyl realizations of Lie algebras and left-right duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Sasa Kresic-Juric, Stjepan Meljanac, Tea Martinic","submitted_at":"2015-11-12T15:56:18Z","abstract_excerpt":"We investigate dual realizations of non--commutative spaces of Lie algebra type in terms of formal power series in the Weyl algebra. To each realization of a Lie algebra $\\g$ we associate a star--product on the symmetric algebra $S(\\g)$ and an ordering on the enveloping algebra $U(\\g)$. Dual realizations of $\\g$ are defined in terms of left--right duality of the star--products on $S(\\g)$. It is shown that the dual realizations are related to an extension problem for $\\g$ by shift operators whose action on $U(\\g)$ describes left and right shift of the generators of $U(\\g)$ in a given monomial. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03936","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"}