{"paper":{"title":"Quantum dynamical Yang-Baxter equation over a nonabelian base","license":"","headline":"","cross_cats":["hep-th","math.SG"],"primary_cat":"math.QA","authors_text":"Ping Xu","submitted_at":"2001-04-06T02:37:44Z","abstract_excerpt":"In this paper we consider dynamical r-matrices over a nonabelian base. There are two main results. First, corresponding to a fat reductive decomposition of a Lie algebra $\\frakg =\\frakh \\oplus \\frakm$, we construct geometrically a non-degenerate triangular dynamical r-matrix using symplectic fibrations. Second, we prove that a triangular dynamical r-matrix $r: \\frakh^* \\lon \\wedge^2 \\frakg$ corresponds to a Poisson manifold $\\frakh^* \\times G$. A special type of quantizations of this Poisson manifold, called compatible star products in this paper, yields a generalized version of the quantum dy"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0104071","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"}