{"paper":{"title":"L\\'evy-Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Adam Skalski, Anna Kula, Biswarup Das, Uwe Franz","submitted_at":"2017-11-07T22:41:29Z","abstract_excerpt":"We study the first and second cohomology groups of the $^*$-algebras of the universal unitary and orthogonal quantum groups $U_F^+$ and $O_F^+$. This provides valuable information for constructing and classifying L\\'evy processes on these quantum groups, as pointed out by Sch\\\"urmann. In the case when all eigenvalues of $F^*F$ are distinct, we show that these $^*$-algebras have the properties (GC), (NC), and (LK) introduced by Sch\\\"urmann and studied recently by Franz, Gerhold and Thom. In the degenerate case $F=I_d$, we show that they do not have any of these properties. We also compute the s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02755","kind":"arxiv","version":4},"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"}