{"paper":{"title":"The Universal $C^*$-Algebra of the Quantum Matrix Ball and its Irreducible $*$-Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Olof Giselsson","submitted_at":"2018-01-31T18:57:01Z","abstract_excerpt":"We prove that any irreducible $*$-representation of $\\mathrm{Pol}(\\mathrm{Mat}_n)_q$ can be 'lifted' to an irreducible *-representation of $\\mathbb{C}[SU_{2n}]_q$, this result is then used to show the existence of the universal enveloping $C^*$- algebra of $\\mathrm{Pol}(\\mathrm{Mat}_n)_q$ and to prove that it is isomorphic to the closure of the image of the Fock representation. Moreover, we also classify all irreducible $*$-representations of $\\mathrm{Pol}(\\mathrm{Mat}_n)_q$ using a diagram approach."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.10608","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"}