{"paper":{"title":"The absolute continuous spectrum of skew products of compact Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DS","math.MP"],"primary_cat":"math.SP","authors_text":"Rafael Tiedra de Aldecoa","submitted_at":"2013-07-28T10:33:15Z","abstract_excerpt":"Let $X$ and $G$ be compact Lie groups, $F_1:X\\to X$ the time-one map of a $C^\\infty$ measure-preserving flow, $\\phi:X\\to G$ a continuous function and $\\pi$ a finite-dimensional irreducible unitary representation of $G$. Then, we prove that the skew products $$ T_\\phi:X\\times G\\to X\\times G,\\quad(x,g)\\mapsto\\big(F_1(x),g\\;\\phi(x)\\big), $$ have purely absolutely continuous spectrum in the subspace associated to $\\pi$ if $\\pi\\circ\\phi$ has a Dini-continuous Lie derivative along the flow and if a matrix multiplication operator related to the topological degree of $\\pi\\circ\\phi$ has nonzero determi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.7348","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"}