{"paper":{"title":"A non commutative K\\\"ahler structure on the Poincar\\'e disk of a C*-algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Esteban Andruchow, Gustavo Corach, L\\'azaro Recht","submitted_at":"2019-07-10T20:32:12Z","abstract_excerpt":"We study the Poincar\\'e disk $\\d=\\{z\\in\\a: \\|z\\|<1\\}$ of a C$^*$-algebra $\\a$ as a homogeneous space under the action of an appropriate Banach-Lie group $\\u(\\theta)$ of $2\\times 2$ matrices with entries in $\\a$. We define on $\\d$ a homogeneous K\\\"ahler structure in a non commutative sense. In particular, this K\\\"ahler structure defines on $\\d$ a homogeneous symplectic structure under the action of $\\u(\\theta)$. This action has a moment map that we explicitly compute. In the presence of a trace in $\\a$, we show that the moment map has a convex image when restricted to appropriate subgroups of $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.04912","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"}