Crystal limits of compact semisimple quantum groups as higher-rank graph algebras
dc.contributor.author | Matassa, Marco | |
dc.contributor.author | Yuncken, Robert | |
dc.date.accessioned | 2023-09-28T14:28:26Z | |
dc.date.available | 2023-09-28T14:28:26Z | |
dc.date.created | 2023-09-26T09:41:52Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 0075-4102 | |
dc.identifier.issn | 1435-5345 | |
dc.identifier.uri | https://hdl.handle.net/11250/3092782 | |
dc.description.abstract | Let Oq [K] denote the quantized coordinate ring over the field C(q) of rational functions corresponding to a compact semisimple Lie group K, equipped with its ∗-structure. Let A0 ⊂ C(q) denote the subring of regular functions at q = 0. We introduce an A0-subalgebra OA0q [K] ⊂ Oq [K] which is stable with respect to the ∗-structure, and which has the following properties with respect to the crystal limit The specialization of Oq [K] at each q ∈ (0,∞) \ {1} admits a faithful ∗-representation πq on a fixed Hilbert space, a result due to Soibelman. We show that for every element a ∈ OA0 q [K], the family of operators πq (a) admits a norm-limit as q → 0. These limits define a ∗-representation π0 of OA0 q [K]. We show that the resulting ∗-algebra O[K0] = π0 (OA0 q [K]) is a Kumjian-Pask algebra, in the sense of Aranda Pino, Clark, an Huef and Raeburn. We give an explicit description of the underlying higher-rank graph in terms of crystal basis theory. As a consequence, we obtain a continuous field ofC∗-algebras (C(Kq ))q∈[0,∞], where the fibres at q = 0 and∞are explicitly defined higher-rank graph algebras. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | De Gruyter | en_US |
dc.relation.ispartofseries | Journal für die Reine und Angewandte Mathematik; | |
dc.title | Crystal limits of compact semisimple quantum groups as higher-rank graph algebras | en_US |
dc.type | Peer reviewed | en_US |
dc.type | Journal article | en_US |
dc.description.version | acceptedVersion | en_US |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 2 | |
dc.identifier.doi | https://doi.org/10.1515/crelle-2023-0047 | |
dc.identifier.cristin | 2178821 | |
dc.source.journal | Journal für die Reine und Angewandte Mathematik | en_US |
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