Fixed-point permanence under actions by finite quantum groups
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908328584544256 |
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| author | Chirvasitu, Alexandru |
| author_facet | Chirvasitu, Alexandru |
| contents | Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously for the two algebras); these include being hyperfinite, atomic, diffuse and of type $I$, $II$ or $III$. Moreover, in all cases the canonical central projections of $M$ and $M^{\mathbb{G}}$ cutting out the summand with the respective property coincide. The result generalizes its classical-$\mathbb{G}$ analogue due to Jones-Takesaki. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_14579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed-point permanence under actions by finite quantum groups Chirvasitu, Alexandru Operator Algebras Functional Analysis Quantum Algebra 20G42, 46L67, 46L10, 16W22, 46L52 Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously for the two algebras); these include being hyperfinite, atomic, diffuse and of type $I$, $II$ or $III$. Moreover, in all cases the canonical central projections of $M$ and $M^{\mathbb{G}}$ cutting out the summand with the respective property coincide. The result generalizes its classical-$\mathbb{G}$ analogue due to Jones-Takesaki. |
| title | Fixed-point permanence under actions by finite quantum groups |
| topic | Operator Algebras Functional Analysis Quantum Algebra 20G42, 46L67, 46L10, 16W22, 46L52 |
| url | https://arxiv.org/abs/2504.14579 |