{"paper":{"title":"A polynomial class of $u(2)$ algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"M. Daoud, W. S. Chung","submitted_at":"2015-12-06T10:57:31Z","abstract_excerpt":"A $r$-parameter ${u}_{\\{\\kappa_1, \\kappa_2, \\cdots, \\kappa_r\\}}(2)$ algebra is introduced. Finite unitary representations are investigated. This polynomial algebra reduces via a contraction procedure to the generalized Weyl-Heisenberg algebra ${\\cal A}_{\\{\\kappa_1, \\kappa_2, \\cdots, \\kappa_r\\}}$ (M. Daoud and M. Kibler, J. Phys. A: Math. Theor. {\\bf 45} (2012) 244036). A pair of nonlinear (quadratic) bosons of type ${\\cal A}_{\\kappa}\\equiv {\\cal A}_{\\{\\kappa_1=\\kappa, \\kappa_2=0, \\cdots, \\kappa_r=0\\}}$ are used to construct, \\`a la Schwinger, a one parameter family of (cubic) $u_{\\kappa}(2)$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.01773","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"}