{"title":"量化同质空间的代数同构","authors":"Robert Yuncken","doi":"arxiv-2409.06139","DOIUrl":null,"url":null,"abstract":"We describe a proof of the following folklore theorem: If $\\cX = G/K$ is the\nhomogeneous space of a simply connected compact semisimple Lie group with\nPoisson-Lie stabilizers, then the $q$-deformed algebras of regular functions\n$\\CC[\\cX_q]$ with $0<q\\leq1$ are mutually non-isomorphic as $*$-algebras.","PeriodicalId":501317,"journal":{"name":"arXiv - MATH - Quantum Algebra","volume":"11 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algebraic isomorphisms of quantized homogeneous spaces\",\"authors\":\"Robert Yuncken\",\"doi\":\"arxiv-2409.06139\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We describe a proof of the following folklore theorem: If $\\\\cX = G/K$ is the\\nhomogeneous space of a simply connected compact semisimple Lie group with\\nPoisson-Lie stabilizers, then the $q$-deformed algebras of regular functions\\n$\\\\CC[\\\\cX_q]$ with $0<q\\\\leq1$ are mutually non-isomorphic as $*$-algebras.\",\"PeriodicalId\":501317,\"journal\":{\"name\":\"arXiv - MATH - Quantum Algebra\",\"volume\":\"11 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Quantum Algebra\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.06139\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Quantum Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.06139","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Algebraic isomorphisms of quantized homogeneous spaces
We describe a proof of the following folklore theorem: If $\cX = G/K$ is the
homogeneous space of a simply connected compact semisimple Lie group with
Poisson-Lie stabilizers, then the $q$-deformed algebras of regular functions
$\CC[\cX_q]$ with $0
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