{"paper":{"title":"Quantum K\\\"ahlerian Lie groups from multiplicative unitaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.OA","authors_text":"F. D'Andrea, P. Bieliavsky, Ph. Bonneau, V. Gayral","submitted_at":"2017-05-23T14:42:44Z","abstract_excerpt":"We show that the deformation theory of Fr\\'echet algebras for actions of K\\\"ahlerian Lie groups developed by two of us, leads in a natural way to examples of non-compact locally compact quantum groups. This is achieved by constructing a manageable multiplicative unitary out of the Fr\\'echet deformation of $C_0(G)$ for the action $\\lambda\\otimes \\rho$ of $G\\times G$ and the undeformed coproduct. We also prove that these quantum groups are isomorphic to those constructed out of the unitary dual $2$-cocycle discovered by Neshveyev and Tuset and associated with Bieliavsky's covariant $\\star$-produ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.08326","kind":"arxiv","version":3},"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"}