{"paper":{"title":"The field of quantum $GL(N,\\mathbb{C})$ in the C$^*$-algebraic setting","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.QA","authors_text":"Kenny De Commer, Matthias Flor\\'e","submitted_at":"2018-02-07T15:40:36Z","abstract_excerpt":"Given a unital $*$-algebra $\\mathscr{A}$ together with a suitable positive filtration of its set of irreducible bounded representations, one can construct a C$^*$-algebra $A_0$ with a dense two-sided ideal $A_c$ such that $\\mathscr{A}$ maps into the multiplier algebra of $A_c$. When the filtration is induced from a central element in $\\mathscr{A}$, we say that $\\mathscr{A}$ is an s$^*$-algebra. We also introduce the notion of $\\mathscr{R}$-algebra relative to a commutative s$^*$-algebra $\\mathscr{R}$, and of Hopf $\\mathscr{R}$-algebra. We formulate conditions such that the completion of a Hopf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02486","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"}