Algebraic isomorphisms of quantized homogeneous spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917772221480960 |
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| author | Yuncken, Robert |
| author_facet | Yuncken, Robert |
| contents | 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 $0<q\leq1$ are mutually non-isomorphic as $*$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic isomorphisms of quantized homogeneous spaces Yuncken, Robert Quantum Algebra Operator Algebras Primary: 20G42, Secondary: 46L67, 17B37 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 $0<q\leq1$ are mutually non-isomorphic as $*$-algebras. |
| title | Algebraic isomorphisms of quantized homogeneous spaces |
| topic | Quantum Algebra Operator Algebras Primary: 20G42, Secondary: 46L67, 17B37 |
| url | https://arxiv.org/abs/2409.06139 |